Past Talks

January 30

(First Week of classes)

February 6 (Meet the Faculty) (Recording)

Vincent Martinez, Hunter College (Department of Mathematics and Statistics)

Title: Parameter Reconstruction for Dynamical Systems

   Abstract: We will talk about the problem of reconstructing unknown parameters in dynamical systems, particularly those induced by evolutionary systems of differential equations (partial and ordinary). We discuss some basic principles and approaches and present both theoretical and computational results. I will also discuss various past and ongoing projects with MA students.

February 13 (Meet the Faculty) (Recording)

Ara Basmajian, Hunter College (Department of Mathematics and Statistics)

Title: Counting Problems, the Modular Group, and Hyperbolic Geometry

     Abstract: The modular group is the group generated by the Möbius group elements z →−1/z and z → z + 1 acting on the upper half-plane. These elements act as isometries with respect to the hyperbolic metric on the upper half-plane, and as a result this group is rich with interesting geometric, number theoretic and combinatorial questions. After introducing hyperbolic geometry and the properties of the modular group, we will discuss various counting problems that arise. These counting problems involve recursion relations, finding roots of polynomials, and using elementary notions from linear algebra.

February 20 (Recording)

   Sathya Chandramouli, University of Massachusetts Amherst (Department of Mathematics and Statistics) 

Title: Dispersive hydrodynamics: from discrete to continuum systems

   Abstract: In this talk, we discuss a collection of recent efforts of the speaker with collaborators in the field of dispersive hydrodynamics. Dispersive hydrodynamics is the study of nonlinear wave dynamics in dispersive (and fluid-like) media. Broadly speaking, dispersive hydrodynamic phenomena are characterized by reciprocal interactions between long (space and time) scale hydrodynamic and short-scale dispersive effects. The dispersive shock wave is a paradigmatic object of study within dispersive hydrodynamics and occurs broadly in fluid mechanics, optics, and superfluidic condensates. In this talk, through the lens of Whitham modulation theory and numerical simulations, we discuss some instances of non-convex dispersive hydrodynamic phenomena in two different physical scenarios of Shock waves (a) in the quantum droplet-bearing environment and (b) the discrete nonlinear Schrödinger equation. Classical, convex dispersive hydrodynamics will be covered first to motivate these non-convex systems

February 27 (Meet the Faculty) (Recording)

   Olga Kharlampovich, Hunter College (Department of Mathematics and Statistics)

Title: Some open problems in group theory and algebra and AI

   Abstract: I will discuss various open problems in group theory and algebra, old and new.  I'll focus on my personal favorites and on what makes these problems captivating.  I'll also talk about problems that can be attacked with AI.

March 6 

(Wednesday Schedule)

March 13 (Recording)

Annie Carter, Northern Arizona University (Department of Mathematics and Statistics)

Title: Two-variable polynomials with dynamical Mahler measure zero

    Abstract: Introduced by Lehmer in 1933, the classical Mahler measure of a complex rational function $P$ in one or more variables is given by integrating $\log |P(z_1, \ldots, z_n)|$ over the unit torus. Lehmer asked whether the Mahler measures of integer polynomials, when nonzero, must be bounded away from zero, a question that remains open to this day. In this talk we generalize Mahler measure by associating it with a discrete dynamical system $f: \mathbb{C} \to \mathbb{C}$, replacing the unit torus by the $n$-fold Cartesian product of the Julia set of $f$ and integrating with respect to the equilibrium measure on the Julia set. We then characterize those two-variable integer polynomials with dynamical Mahler measure zero, conditional on a dynamical version of Lehmer's conjecture.

March 20 (Recording)

   Zhuolin Qu, The University of Texas at San Antonio (Department of Mathematics)

Title: Title: Multistage Spatial Model for Informing Release of Wolbachia-Infected Mosquitoes as Disease Control

   Abstract: Wolbachia is a natural bacterium that can infect Aedes mosquitoes and block the transmission of mosquito-borne diseases, including dengue fever, Zika, and chikungunya. Field trials have been conducted worldwide to suppress local epidemics. We present a new partial differential equation model for the spread of Wolbachia infection in mosquitoes. The model accounts for both the complex Wolbachia vertical transmission cycle and detailed life stages in the mosquitoes, and it also incorporates the spatial heterogeneity created by mosquito dispersion in the two-dimensional release domain. Field trials and previous modeling studies have shown that the fraction of infection among mosquitoes must exceed a threshold level for the infection to persist. We use the spatial model to identify a threshold condition for having a self-sustainable Wolbachia infection in the field. When above this threshold, the model gives rise to a spatial wave of Wolbachia infection. We quantify how the threshold condition and invasion velocity depend on the diffusion process and other model parameters, and we study different intervention scenarios to inform the efficient releases.

March 27 (Recording)

Suleyman Taspinar, Queens College, CUNY (Department of Economics)

Title: Specification and Estimation of Matrix Exponential Social Network Models with an Application to Add Health Data

    Abstract: In this paper, we introduce a new specification for modeling peer effects due to social interactions. We refer to this specification as the matrix exponential social (MES) network model. The MES network model allows for the endogenous effect, the contextual effects, heterogeneity across groups, the correlation in unobserved characteristics of members, as well as an unknown form of heteroskedasticity. We propose consistent estimation and inference methods for the MES network model. In an extensive simulation study, we show that the proposed methods perform satisfactorily. In an empirical application using the Add Health data, we illustrate how the MES network model can be used in identifying peer effects on academic success, recreational activities and smoking frequency of adolescents.  This is joint research with Ye Yang and Osman Dogan.

April 3

Thomas Mathew, Tech Lead (Cisco Systems)

(Re-scheduled to May 10, MA Student Presentation Day)

Title: Mixture Models and Network Threats

        Abstract: Security teams managing large computer networks can face upwards of hundreds of security alerts in a day. The volume of alerts leads to alert fatigue and an inability to properly triage on alerts. Security teams would like a system that helps prioritize and rank the importance of alerts. An algorithm that segments alerts based on behavioral characteristics provides the starting point to solve the security team's dilemma. Today's talk presents one such method to segment network traffic via a multinomial mixture model. We'll go over modelling choices that led to selecting a mixture model for the data as well as an analysis of the parameter estimation required to build the model. The multinomial mixture model readily captures the count based nature of the alerts and identifies segments that represent behavioral patterns of interest. We identify six behavioral patterns that are present in all large corporate networks and represent different types of network threats (botnets, ransomware, etc). 

April 10 (Recording)

Xin Ma, Columbia University (Department of Biostatistics)

Title: Statistical Approaches to Neuroimaging: Prediction, Feature Selection, and Interpretability

    Abstract: Neuroimaging data has become a vital resource for identifying biomarkers associated with neurocognitive development and disease. In this talk, I will introduce the structures and unique characteristics of MRI and functional MRI (fMRI) data. I will then present two projects that focus on prediction and feature selection using various types of neuroimaging data. These projects employ methodologies including functional data analysis, high-dimensional statistics, and deep learning models with a focus on interpretability. Through these discussions, I will underscore how statistical modeling enhances neuroimaging analysis and contributes to a deeper understanding of brain function.

April 17

(Spring break)

April 24 (Recording)

Shirshendu Chatterjee, Graduate Center and City College, City University of New York (Department of Mathematics)

Title: Phase transitions in long-range versions of first passage percolation models

    Abstract: The first passage percolation model has been classically studied in nearest neighbor settings. In this model, each of the ages of a ground graph is assumed to have a positive random weight (passage time), which is drawn independently from a common distribution. One of the main objectives is to understand the asymptotic behavior of the associated (random) metric given by the minimum time (called first-passage time) to communicate between two distant nodes of the ground graph.  In many applications, certain long-range versions of the first-passage percolation turn out to be a natural model. In these versions, long-range edges can also be used for communications in addition to the nearest neighbor ones. In this talk, we will discuss two such versions and see the phase transitions in the asymptotic behavior of the associated random metric depending on the nature of the long-range transmission pattern.

May 1 (Meet the Faculty)

Olympia Hadjiliadis, Hunter College (Department of Mathematics and Statistics)

Title: A Speed-based Estimator of Signal-to-Noise Ratios

    Abstract: We present an innovative estimator of the signal-to-noise ratio (SNR) in a Brownian motion model. That is, the ratio of the mean to the standard deviation of the Brownian motion. Our method is based on the method of moments estimation of the drawdown and drawup speeds in a Brownian motion model, where the drawdown process is defined as the current drop of the process from its running maximum and the drawup process is the current rise of the process above its running minimum. The speed of a drawdown of K units (or a drawup of K units) is then the time between the last maximum (or minimum) of the process and the time the drawdown (or drawup) process hits the threshold K. We compare our estimator to traditional ones. Numerical results show that our estimator consistently outperforms some traditional estimators but not the uniformly minimum-variance unbiased estimator. However, we discuss cases in which the statistic related to our estimator can be useful. This is when the SNR changes in a real-time observation stream and the problem is jointly detecting and estimating the pre-and-post SNR’s. We finally present the asymptotic distribution of our estimator. This is joint work with Yuang Song (Columbia University, Teachers College).

May 8 (Recording)

Maggie Habeeb, PennWest (Department of Chemistry, Mathematics and Physics) 

Title:  Groups in Post-quantum Cryptography

    Abstract:  The security of RSA and the Diffie-Hellman Key Exchange protocols is based on "hard" number theoretical problems. With Shor's algorithm and the prospect of a quantum computer, the security of these schemes is theoretically questionable. This prompted the search for alternative cryptographic schemes, which resulted in the field of post-quantum group-based cryptography. In this talk, we will provide an overview of the field with some examples of proposed schemes and the cryptanalysis of the schemes.

Saturday, May 10

Mathematics and Statistics Student Research Presentation Day

May 15 

(Last Week of classes)

August 29

(First Week of Classes)

September 5 (Meet the Faculty)

Peter Craigmile (Hunter, Department of Mathematics and Statistics) (Recording)

Title: Statistical modeling in space and time 

Abstract: In Fall 2023 I started at a professor in this department, after spending over two decades at The Ohio State University.  I am interested in developing statistical analysis methods for analyzing data observed in space and time. In this presentation, I will summarize three different projects that I recently been a part of that require the development of statistical models and tools to help people solve problems in climate science, environmental health, and public health.   I suggest some opportunities for MA projects in our department.

September 12 (Meet the Faculty)

Vincent Martinez (Hunter, Department of Mathematics and Statistics) (Recording)

Title: The Secret Life of Mathematical Fluid Dynamics

Abstract: Fluids influence our lives in a multitude of ways, ranging from the mundane (when we stir milk into our coffee) to the spectacular (the formation of galaxies). It is a great achievement of the human intellect that we are able to study such phenomenon abstractly through mathematics. This talk will describe how fluids can be studied mathematically and introduce a few interesting problems, both theoretical and practical, of ongoing scientific relevance, some of which students at Hunter can study with the speaker.

September 19 (Meet the Faculty)

Barry Cherkas (Hunter, Department of Mathematics and Statistics) (Recording)

Title: Sketching without Technology

Abstract: This talk is about a new tool to add to the toolkit for sketching without technology. It is shown that any factored algebraic function can be hand- sketched straightforwardly, at the precalculus level. The procedure calls for functions to be rewritten in what we call zeros-ordered factoring, where the factors are listed in the order of their distinct real zeros. This factoring leads to an efficient procedure to create a sign chart, using only mental arithmetic and basic mathematical reasoning. The method offers an alternative to the traditional method for solving algebraic inequalities, which requires paper-and-pencil computations. The sign charts also identify what we call no-graph regions that guide hand sketching at function zeros. The no-graph regions visually resolve the direction of crossing, or not, the x-axis at function zeros as well as the direction of any vertical asymptotic behaviors at infinite discontinuities. A representative sketch can then be refined with calculus to get a complete calculus hand sketch.

Dana Sylvan (Hunter, Department of Mathematics and Statistics)

Title: A selection of past student projects

Abstract:  This is a brief presentation of case studies and data analysis reports written by some of the graduate students that I worked with here at Hunter over the past two decades. 

September 26 

Geremias Polanco (Smith College, Department of Mathematical Sciences) (Recording)

Title: On Numbers… and Patterns… and Games… and Greed 

Abstract: Two sequences are complementary if their union gives the positive integers and their intersection is empty. For instance, the even and odd numbers are two complementary sequences. Similarly, the prime and composite numbers form another pair of complementary sequences. Combinatorial Games are two player (usually alternating), deterministic games (no flipping coins, tossing dice, ...) and with perfect information (each player knows all information available about the state of the game. Nothing is hidden). On the other hand continued fractions are a special type of fractions that form under the following rules: "add a fraction to an existing fraction’s denominator." In this talk we will present some old and new results about complementary sequences, see how some of they arise as winning strategies for combinatorial games and how these sequences relate to continued fractions and other mathematical objects like dynamical systems.

October 3

(Rosh Hashanah)

October 10

Robin Wilson (Loyola Marymount University, Department of Mathematics and Statistics) (Recording)

Title: Mathematical microaggressions and their impact on students’ sense of belonging in the mathematics classroom.

Abstract: Microaggressions are intentional or unintentional actions that communicate hostile, derogatory, or negative messages towards a recipient (Sue et al., 2007).  Microaggressions that students receive in a math class can impact a students’ learning experience and sense of belonging.  We will discuss our analysis of the reflections of 133 undergraduate math students who were asked to reflect on an article about Mathematical Microaggressions (Su, 2015).   Findings show that a majority of the students in our study reported experiences that made them feel like they do not belong in the math classroom, and that racial, gendered, and mathematical microaggressions contribute to this.  We will also share some ideas for affirming students’ sense of belonging in the math classroom through microaffirmations.  This research supports the need to develop initiatives at departmental and institutional levels to encourage more inclusive spaces in math and STEM classrooms. 

October 17

Alina Vdovina (City College, Department of Mathematics) (Recording)

Title:  Buildings, quaternions and Drinfeld-Manin solutions of Yang-Baxter equations.

Abstract: We will give a brief introduction to the theory of buildings and present their geometric, algebraic and arithmetic aspects. In particular, we present explicit constructions of infinite families of quaternionic cube complexes, covered by buildings. We will use these cube complexes to describe new infinite families of Drinfeld-Manin solutions of Yang-Baxter equations. 

October 24 (Meet the Faculty)

Tatyana Khodorovskiy (Hunter, Department of Mathematics and Statistics) (Recording) (Slides)

Title: Twists and Turns: Enumerating the topological classes of knots/links on a 9x9x9 Rubik’s cube

Abstract: In this talk, I will discuss joint work with David Plaxco, where we classify and enumerate the possible topological classes of “photogenic knots” that can be depicted on a 9-layered Rubik’s cube, with a certain edge permutation. This talk should be accessible to undergraduates.

October 31 (Meet the Faculty)

Martin Bendersky (Hunter, Department of Mathematics and Statistics) (Recording)

Title: How a topologist looks at data

Abstract: Data is often endowed with a metric, i.e., a notion of a distance between the data points.  I will describe how this information produces a geometric object called the Vietoris-Rips complex of the data.    I will illustrate the construction using a metric inspired by coding theory.

November 7 (Meet the Faculty)

Indranil SenGupta (Hunter, Department of Mathematics and Statistics) (Recording)

Title: From pixels to profit: a merger of mathematics, finance, and data science

Abstract: Mathematical finance is a highly exciting area of applied mathematics. In this talk, at first, I will present some basic topics in mathematical finance such as time value of money, “no arbitrage opportunity” (“there is no free lunch!”), delta hedging, forward contracts, binomial model, options and classical Black-Scholes equation. Modern finance is entirely data driven and it is crucial to incorporate various data-science-based techniques to existing stochastic models. This will lead to the possibility of several MS projects. As an example, I will show the results from a project where we implement some "image-based" techniques for estimating rare events in financial time series. We employ specific neural networks to recognize patterns in financial "photos", followed by a bootstrapped image similarity distribution to predict unusual events relevant to financial market analysis.

November 14 (Meet the Faculty)

Ilya Kapovich (Hunter, Department of Mathematics and Statistics) (Recording)

Title: Counting closed geodesics in the moduli space of Outer space: double exponential growth

Abstract: Exponential growth is ubiquitous in mathematics, physics, biology, finance and other areas. It is also interesting to look for natural examples of systems exhibiting faster than exponential growth.  A classic result of Margulis from the 1970s shows that the number of closed geodesics of length at most L on a compact manifold of negative curvature (such as a hyperbolic surface) grows exponentially in L, with the growth rate precisely controlled by a certain entropy constant. In 2011 Eskin and Mirzakhani obtained an analog of Margulis' result for counting closed geodesics in the moduli space of hyperbolic structures on a compact surface. We consider a related setting of the moduli space of metric graphs, which arises from the so-called Culler-Vogtmann Outer space. It turns out that for this moduli space the number of closed geodesics grows doubly exponentially fast. The setting exhibits some other novel features not seen in classical hyperbolic dynamics. This talk is based on joint work with Catherine Pfaff.

November 21

Xiang Wan (Loyola University Chicago, Department of Mathematics and Statistics) (Recording)

Title: 2D Laplace Equations with Line Fracture: from Qualitative to Quantitative Analysis

Abstract: In this talk, we investigate a partial differential equation (PDE), more specifically, the 2D Laplace equation with the forcing term being a Dirac delta function on a line segment, modeling a singular line fracture. Numerically, such a fracture imposes additional treatment of the meshing while constructing the triangular Finite Element space. Inspired by the 1D case, we can see that a graded meshing is naturally called for, where the level of grading depends on the distance to the fracture.

To tune the numerical analysis of this system with the 'best' level of grading to get the optimal convergence rate, one has to look closer into the regularity of the solution in weighted Sobolev spaces - in contrast to the regularity results in standard Sobolev spaces from the classic Elliptic theory of PDEs. Such examination reveals deeper connections between the qualitative regularity and quantitative behavior of the system.  Last but not least, we will present how the characteristics, and lack thereof, of different geometries of domains plays a role via numerical demonstrations.

November 28

(Thanksgiving Break)

December 5

Krutika Tawri (UC Berkeley, Department of Mathematics) (Recording)

Title: Stochastic and deterministic moving boundary problems.

Abstract: In this talk we will discuss recent results concerning stochastic (and deterministic) moving boundary problems, particularly arising in fluid-structure interaction (FSI), where the motion of the boundary is not known a priori. Fluid-structure interaction refers to physical systems whose behavior is dictated by the interaction of an elastic body and a fluid mass and it appears in various applications, ranging from aerodynamics to structural engineering. Our work is motivated by FSI models arising in biofluidic applications that describe the interactions between a viscous fluid, such as human blood, and an elastic structure, such as a human artery. To account for the unavoidable numerical and physical uncertainties in applications we analyze these PDEs under the influence of external stochastic (random) forces. 

We will consider nonlinearly coupled fluid-structure interaction (FSI) problems involving a viscous fluid in a 2D/3D domain, where part of the fluid domain boundary consists of an elastic deformable structure, and where the system is perturbed by stochastic effects. The fluid flow is described by the Navier-Stokes equations while the elastodynamics of the thin structure are modeled by shell equations. The fluid and the structure are coupled via two sets of coupling conditions imposed at the fluid-structure interface. We will consider the case where the structure is allowed to have unrestricted deformations and explore different kinematic coupling conditions (no-slip and Navier slip) imposed at the randomly moving fluid-structure interface, the displacement of which is not known a priori. We will present our results on the existence of (martingale) weak solutions to the (stochastic) FSI models. This is the first body of work that analyzes solutions of stochastic PDEs posed on random and time-dependent domains and a first step in the field toward further research on control problems, singular perturbation problems etc. We will further discuss our findings, which reveal a novel hidden regularity in the structure’s displacement. This result has allowed us to address previously open problems in the 3D (deterministic) case involving large vectorial deformations of the structure. We will discuss both the cases of compressible and incompressible fluid.

December 12

(Last week of classes; study for Finals!)

December 19

Ozlem Ugurlu (St. Louis University, Department of Mathematics and Statistics) (Recording)

Title: Irreducibility of Hessenberg Varieties

Abstract: Hessenberg varieties are subvarieties of the flag variety, and they arise in many areas, such as representation theory, algebraic geometry, and combinatorics. For this reason, Hessenberg varieties have been extensively studied yet still many questions remain open.

In this talk, I will answer some questions about Hessenberg varieties associated with semisimple operators having two eigenvalues, using results from the theory of orbit closure of a spherical subgroup of the general linear group. I will introduce combinatorial objects called clans, which are used for parameterizing such orbit closures. Then, I will explain how these clans occur in Hessenberg varieties and give a criterion for identifying irreducible Hessenberg varieties. This talk is based on joint work with joint work with Mahir Bilen Can, Martha Precup, and John Shareshian.

January 25

(Start of classes)

February 1

Rob Thompson (CUNY Hunter, Department of Mathematics and Statistics) Recording

Title: A report on the Mathematical Association of America’s studies on college calculus instruction and a summary of best practices

Abstract: The Mathematical Association of America conducted two extensive, NSF funded, studies of calculus instruction in American colleges and universities, the first of their kind. The first study took place from 2010-2015 and surveyed students and faculty from a large random sample of schools, collecting much data on who takes calculus, and how it is taught.  The study also included case studies from over 20 schools.   This study led to the formulation of seven “best practices”.

The second MAA study took place from 2015-2020 and involved a survey of all 330 graduate awarding mathematics departments in the US, along with case studies from around a dozen schools to examine the ways in which schools have implemented the seven best practices and to measure the effects of  changes made. 

In this talk I will report on some of the results from these studies.

February 8

Daniel Grange (SUNY Stony Brook, Department of Applied Mathematics) Recording

Title: Optimal Transport: Introduction and applications in filtering on Riemannian manifolds

Abstract: A few years before the French Revolution, Gaspard Monge introduced optimal transport, the problem of minimizing the average cost of transporting soil from the ground, deblais, to build fortifications, remblais. 150 years later Leonid Kantorovich characterized the problem in an economics setting, for which he later won the nobel prize. In this talk, I will discuss the evolution of the optimal transport problem, and how modern luminaries like Brenier and McCann, enable the computation of optimal transport maps on Riemannian manifolds for the use of sampling conditional probability distributions.

February 15

(Hiatus) 

February 22

(Monday schedule)

February 29

Kisung You (CUNY Baruch, Department of Mathematics) In-Person, HE 920

Title: Towards non-Euclidean space : an example of median

Abstract: A major trajectory in the development of statistics has been extending the scope of mathematical spaces behind the data we observe, from numbers to vectors, functions, and beyond. This has sparked both theoretical and computational breakthroughs. In this talk, I revisit the median, a robust alternative to the mean, as an example and introduce a novel extension of the concept in the space of probability measures under the framework of optimal transport. 

March 7

Ran Wei (Researcher at Verses AI) Recording

Title:  Developing resource-bounded adaptive agents with a single objective function

Abstract: Adaptive agents that can automate and augment human capabilities are of primary interest in current AI research. However, how to develop such agents in terms of choosing the appropriate decision variables, constraints, and objective functions has been an open question. Using the language of reinforcement learning and optimal control, I discuss a line of research aiming to develop resource-bounded agents with a single objective function and as a result eliminate catastrophes caused by training agent components on misaligned objectives. 

March 14

Silvia Ghinassi (University of Washington, Department of Mathematics) In-Person, HE 920

Title: Self-similar sets and Lipschitz graphs

Abstract: A one dimensional set is said to be purely unrectifiable if it has almost no shadows. In other words, if its intersection with any Lipschitz graph has measure zero. At what dimension do purely unrectifiable sets and Lipschitz graphs actually see each other? After a few preliminary answers, we will present the construction of Lipschitz graphs that intersect purely unrectifiable sets at high dimensions. We first take into account the special case of the four corner Cantor set and then generalize our construction for self similar sets, i.e. attractors of general iterated function systems satisfying a certain separation condition. I will include plenty of pictures and try to keep the talk accessible to a general audience of mathematicians. This is ongoing joint work with Blair Davey and Bobby Wilson.

Recording of a similar talk (missing intro).

Recording of a similar talk targeting experts.

Recording of short recording on the Analyst's Traveling Salesperson Theorem. 

Recording of an informal introduction to Geometric Measure Theory and Dimension.

March 21

(Hiatus)

March 28

Robert Ghrist (University of Pennsylvania, Department of Mathematics) In-person, Hemmerdinger Screening Room, HE 706

Title:  Opinion Dynamics on Sheaves

Abstract: There is a long history of networked dynamical systems that  models the spread of opinions over social networks, with the graph Laplacian playing a lead role.  One of the difficulties in modelling opinion dynamics is the presence of polarization: not everyone comes to consensus. This talk will describe work with Jakob Hansen introducing a new model for opinion dynamics using sheaves of vector spaces over social networks. The graph Laplacian is enriched to a Hodge Laplacian, and the resulting dynamics on discourse sheaves can lead to some very interesting and perhaps more realistic outcomes.  Extensions of these ideas will also be surveyed.

April 4

(Hiatus) 

April 11

(Hiatus) 

April 18

Jeremy Melvin (Open Block Labs) Recording

Title: A Mathematical Modeling Example: Sybil Detection in Crypto Protocols

Abstract: A sybil attack is where multiple entities, all operated by a single actor, masquerade as distinct individuals in order to exploit a system. These can be especially problematic for Crypto protocols attempting to provide rewards to their early users.  To combat this, using a combination of mathematical tools and machine learning methods, detection algorithms can be developed to cluster and classify entities.  First, I will provide some initial background on blockchains, decentralized apps and the airdrop mechanism.  Then, using the goal of sybil detection, I will go through the development process and the background and tools I rely on when approaching a problem as a data scientist/mathematical modeler.

April 25

(Spring break)

May 2

(Hiatus)

May 9

Dorit Hammerling (Colorado School of Mines) In-Person, HE 920

Title: Quality Assurance for Earth System Models: a new statistical testing framework


Abstract: State-of-the-science climate models are valuable tools for understanding past and present climates and are particularly vital for addressing otherwise intractable questions about future climate scenarios.  The National Center for Atmospheric research leads the development of the popular Community Earth System Model (CESM), which models the Earth system by simulating the major Earth system components (e.g., atmosphere, ocean, land, river, ice, etc.) and the interactions between them.  These complex processes result in a model that is inherently chaotic, meaning that small perturbations can cause large effects.  For this reason, ensemble methods are common in climate studies, as a collection of simulations are needed to understand and characterize this uncertainty in the climate model system.  While climate scientists typically use initial condition perturbations to create ensemble spread, similar effects can result from seemingly minor changes to the hardware or software stack.  This sensitivity makes quality assurance challenging, and defining “correctness” separately from bit-reproducibility is really a practical necessity. Our approach casts correctness in terms of statistical distinguishability such that the problem becomes one of making decisions under uncertainty in a high-dimensional variable space.  We developed a statistical testing framework that can be thought of as hypothesis testing combined with Principal Component Analysis (PCA). One key advantage of this approach for settings with hundreds of output variables is that it not only captures changes in individual variables but the relationship between variables as well. This testing framework referred to as “Ensemble Consistency Testing” has been successfully implemented and used for the last few years, and we will provide an overview of this multi-year effort and highlight ongoing developments including a generalization to a broad class of numerical models with spatio-temporal output.

May 16 & May 28 (BA and MA Student Research Talks) May 16 Recording & May 28 Recording

May 16: Sanjay Bajnath & Alsu Flare (Hunter College)

Topics: Steady State Solutions of the Generalized 2D Euler Equations with Finite Frequency Support (Sanjay Bajnath), Generalized Sabra Shell Models for Turbulence (Alsu Flare)

May 28: Nakul Thampy, Edgar Cuapio-Diaz, Katie Trimper, and Jin Rong Zheng (Hunter College)

Topics: Vanishing Viscosity Limit for Dyadic Models of Turbulence (Nakul Thampy), Identifying Optimal Thresholds for SINDy (Edgar Cuapio-Diaz and Jin Rong Zheng), Effects of Noisy Data in SINDy (Katie Trimper)

September 31 - October 5 

(Hiatus)

October 12

Adam Larios (University of Nebraska-Lincoln)

Title: Can Flaming Differential Equations Explode?

Abstract: Partial Differential Equations (PDE) lie at the heart of nearly every area of science.  Einstein's theory of general relativity, quantum mechanics, complex weather patterns, the spread of disease, the turbulent flow of blood in the heart, the growth of tumors, the stability of bridges, the erratic patterns of stock options, the pulsing of electromagnetic waves, the flow of oceans and rivers, the flocking patterns of birds, the growth of bones as we develop, the spots of cheetahs, and the stripes of zebras, are all modeled by PDEs.  Moreover, PDEs arise within mathematics itself, in areas such as differential geometry (the minimal surface equation), complex analysis (the Cauchy-Riemann equations), and harmonic functions (Laplace's equation).  Two of the seven famous $1,000,000 Clay Millennium Prize problems are directly about PDEs, and a third problem was solved by using PDEs as the major proof tool.  

I will give many examples of PDEs, and then give you a few tools for being able to understand much of the basic behavior of PDEs at a glance.  We will see many visual demonstrations, and by the end, you will be able to understand some of the underlying dynamics of several important PDEs, including the "flame equation", also known as the Kuramoto-Sivashinsky equation (KSE).  We will discuss the problem of singularities for this equation in 2D, that is, the question of whether solutions to the flame equation can explode.  Most of the talk should be accessible to students who have taken calculus.

October 19 

(Hiatus)

October 26

Robyn Brooks (ICERM at Brown University)

Title: Computing the Rank Invariant and the Matching Distance of Multi-Parameter Persistence Modules (with the help of discrete Morse theory)

Abstract: Persistent Homology is a tool of Computation Topology which is used to determine the topological features of a space from a sample of data points.  In this talk, I will introduce the (multi-)persistence pipeline, as well as some basic tools from Discrete Morse Theory which can be used to better understand the multi-parameter persistence module of a filtration. In particular, the addition of a discrete gradient vector field consistent with a multi-filtration allows one to exploit the information contained in the critical cells of that vector field as a means of enhancing geometrical understanding of multi-parameter persistence. I will present results from joint work with Claudia Landi, Asilata Bapat, Barbara Mahler, and Celia Hacker, in which we are able to show that the rank invariant for nD persistence modules can be computed by selecting a small number of values in the parameter space determined by the critical cells of the discrete gradient vector field. These values may be used to reconstruct the rank invariant for all other possible values in the parameter space.  Time permitting, I will also introduce results from a subsequent work, in which we provide theoretical results for the computation of the matching distance in two dimensions.

November 2

Laurentiu Hinoveanu (University of Kent at Canterbury) Recording

Title: Performance monitoring in anti-doping with Bayesian longitudinal models 

Abstract: In the fight against doping, there is an increasing need to develop methods which allow one to sensibly allocate testing resources. As the primary reason for doping is the improvement of athletic performance, it is reasonable to suggest that monitoring an individual's competition results on a longitudinal basis may reveal suspicious performance improvements. This work is an extension of a recently published performance model which aims to distinguish between normal or expected rates of progression and those caused by doping. We build a Bayesian spline model which also allows for skewed or heavy-tailed data. These assumptions lead to more robust estimators in the presence of poor performances. We find that athletes’ trajectories follow a similar pattern, across performances in different sports measured by distance, time, or weight. We use our model to identify changes in the career performance trajectory of an athlete that may not be consistent with their age-matched cohort. These athletes can be flagged as individuals who may be at greater risk for doping and warrant follow-up investigation. We evaluate the performance of this approach on two data sets of athlete performances. 

Co-authors: Professor Jim Griffin (University College London), Professor James Hopker (University of Kent)

November 9 

(Hiatus)

November 16

Vaishavi Sharma (Ohio State University) Recording

Title:  p-adic valuations of integer sequences and their properties. 

Abstract: Given a prime p and any positive integer n, the p-adic valuation of n, denoted by \nu_p(n), is the highest power of p that divides n. This notion is extended to \mathbb{Q} by \nu_p(\frac{a}{b})=\nu_p(a)-\nu_p(b) and by setting \nu_p(0) = \infty. For any sequence \{a_n\} and a fixed prime p, the sequence of valuations \nu_p(a_n) often presents interesting challenges. In this talk, I will discuss p-adic valuations of some common integer sequences and some interesting properties. 

November 23

(Thanksgiving Holiday)

November 30

Sarah Strikwerda (University of Pennsylvania) Recording

Title: Optimal control of fluid flow through deformable porous media

Abstract: Poroelasticity refers to fluid flow through deformable porous media such as soil or biological tissues. Equations describing this process have been studied in order to gain understanding of a variety of applications including questions related to petroleum engineering and fluid flow in biological applications. We focus on the Lamina Cribrosa which is the primary location where damage related to glaucoma occurs. We seek to control the fluid pressure and how the solid moves using mathematical techniques.

December 7

Marco Carfagnini (University of California-San Diego) Recording

Title: Brownian motion, small ball probabilities, and infinite dimensional spaces. 

Abstract:  In this talk we will discuss stochastic processes, and in  particular Brownian motion. This process is named after botanist Robert Brown who noticed pollen grains moving on the surface of water. We will see how this process relates to the so-called random walk; and how surprising connections to differential equations (i.e. eigenvalue problems) and   infinite dimensional  objects (paths spaces) arise.  The talk does not require a background in probability and everyone is welcome to attend. 

December 14

Paolo Piersanti (Indiana University-Bloomington) Recording

Title: Obstacle Problems in Linearised Elasticity: Theory and Numerical Analysis

Abstract: In this talk, I will present two results concerning the numerical approximation of the solution of obstacle problems for shells. In the first part of the talk, I will present a result establishing a convergent numerical scheme for approximating the solution of an elliptic variational inequality modelling the deformation of a linearly elastic elliptic membrane shell subject not to cross a prescribed flat obstacle. Numerical simulations will corroborate the aforementioned theoretical results. In the second part of the talk, I will present another method, based on Enriching Operators, for establishing the convergence of a numerical scheme approximating the solution of an obstacle problem for linearly elastic shallow shells.

February 2 Zoom (Recording)

Selvi Kara (University of Utah, Science Research Initiative Fellow)

Monomial ideals: a bridge between algebra and combinatorics

One of the central problems in commutative algebra concerns understanding the structure of an ideal in a polynomial ring. Abstractly, an ideal's structure can be expressed through an object called its minimal resolution, but there is no explicit method to obtain a minimal resolution in general, even for the simpler and fundamental class known as monomial ideals. In this talk, we will focus on resolutions of monomial ideals. In particular, I will introduce a new combinatorial method that provides a resolution of any monomial ideal using tools from discrete Morse theory. 

February 9 Zoom (Recording)

Patrick Phelps (University of Arkansas, Department of Mathematical Sciences)

Quantifying non-uniqueness in the Navier-Stokes local energy class using Picard Iteration

We investigate non-unique solutions to the 3D incompressible Navier-Stokes equations. In some settings, non-uniqueness for forced, and non-forced Navier-Stokes has been affirmed. Within the Leray class, numerical simulations constructing non-unique, scaling invariant solutions from the same initial data support conjectured non-uniqueness. In this talk, we take the perspective that solutions in the local energy class are non-unique and quantify what we call the `separation rate' of two scaling invariant solutions with the same data. We begin by showing decay rates for solutions with locally subcritical data, then extend these to decay rates of approximations by Picard iterates. From this we may bound the rate at which the pointwise difference of two solutions can grow in time. We then show we are almost able to recover this, locally, in some critical classes, without any scaling assumptions.

February 16 Zoom (Recording)

Daniel A. Cruz (University of Florida, Laboratory for Systems Medicine)

Topological data analysis of pattern formation in stem cell colonies

Confocal microscopy imaging provides valuable information about the current expression states within in vitro cell cultures. However, few tools exist to quantify the spatial organization of the cells observed in these images. In this talk, we focus on studying the pattern formation of human induced pluripotent stem cell (hiPSC) cultures, which have become powerful, patient-specific test beds for investigating the early stages of embryonic development. We present a modular, general-purpose pipeline that extracts cell-specific signal intensities from confocal microscopy images. The pipeline then assigns cell types based on corresponding intensities and quantifies spatial information among cell types through topological data analysis (TDA). We provide an overview of TDA and discuss the biological insights which we gain from applying our pipeline to microscopy images of hiPSC colonies, including the detection and quantification of changes in pattern formation caused by cell-to-cell signaling and differentiation.

February 23, March 2 

Hiatus

March 9 Zoom (Recording)

Brendan Kelly (Harvard University, Department of Mathematics)

Refocusing introductory math courses on modeling. 

Introductory mathematics courses have the potential to equip students with the knowledge, skills, and dispositions necessary to solve important problems our world faces. Despite this incredible potential to create transformative educational experiences, students often encounter introductory mathematics courses as a burdensome requirement. In this presentation, I will share my experience of reimagining my introductory calculus course as a mathematical modeling course. I will discuss leading design principals, share concrete tasks, and provide some data on student outcomes. I am eager to collect feedback, find inspiration, and meet new collaborators.

March 16 Zoom (Recording)

Ajmain Yamin (CUNY Graduate Center, Department of Mathematics)

The Accelerated Zeckendorf Game

The Zeckendorf decomposition of a positive integer n is the unique set of nonconsecutive Fibonacci numbers that sum to n. Baird-Smith et. al. defined a game on Fibonacci decompositions of n called the Zeckendorf Game. In this talk, I will speak about a new variant of the Zeckendorf Game, called the Accelerated Zeckendorf Game, in which a player may play as many moves of the same type as possible on their turn. The Accelerated Zeckendorf Game was introduced and investigated by undergraduates Diego Garcia-Fernandezsesma (Boston University), Thomas Rascon (UCSD) and Risa Vandergrift (University of Minnesota) in the 2022 Polymath Jr program. This work was mentored by Prof. Steven J. Miller (Williams College) and myself (CUNY Graduate Center). 

March 23 Zoom (Recording)

Quyuan Lin (University of California Santa Barbara, Department of Mathematics)

Title: Primitive equations: mathematical analysis and machine learning algorithm

Large scale dynamics of the ocean and the atmosphere are governed by the primitive equations (PE). In this presentation, I will first review the derivation of the PE and some well-known results for this model, including well-posedness of the viscous PE and ill-posedness of the inviscid PE. The focus will then shift to discussing singularity formation and the stability of singularities for the inviscid PE, as well as the effect of fast rotation (Coriolis force) on the lifespan of the analytic solutions. Finally, I will talk about a machine learning algorithm, the physics-informed neural networks (PINNs), for solving the viscous PE, and its rigorous error estimate.

March 30 

Hiatus

April 6, April 13

Spring Break

April 20 Zoom (Recording)

Cooper Boniece (University of Utah, Department of Mathematics)

Change-point detection in high dimensions with U-statistics 

The problem of detecting change points in otherwise statistically homogeneous sequences of data arises in countless applications across the sciences. However, in high-dimensional settings where the dimension of the observed data is comparable to or much larger than the sample size, many classical approaches to this problem suffer from theoretical and/or practical drawbacks even under idealized independence assumptions. In this talk, I will discuss some recent work concerning a nonparametric change-point detection method that retains favorable asymptotic properties in high dimensions, and will illustrate some of its advantages compared to existing approaches in the literature. This talk is based on joint work with Lajos Horváth and Peter Jacobs.

April 27 

Hiatus

May 4 Zoom (Recording)

Kurt Butler (SUNY Stony Brook, Department of Electrical and Computer Engineering)

Machine learning with Gaussian processes

Gaussian processes (GPs) are random processes (also called random fields) that can be used to place a probability distribution over spaces of functions. Combined with Bayes theorem, GPs become an extremely powerful method for nonparametric regression, i.e. learning functions from data in an unconstrained manner. In this talk, we will introduce the basics of GP theory. Then we will touch on many interesting uses of GPs, including Bayesian optimization, active inference, latent variable models, and estimating derivatives. This talk is based on ongoing research with Dr. Guanchao Feng and Dr. Petar Djuric at Stony Brook University.

May 11 Zoom (Recording)

Dalton Sakthivadivel (VERSES Research Lab and Laufer Center for Physical and Quantitative Biology at Stony Brook University)

Path-wise large deviations theory and some of its applications

Since the work of Ellis in the eighties, we have known that large deviations theory gives us a natural way of making the sorts of asymptotic statements about probability which are often found in equilibrium statistical physics. Today large deviations theory remains a promising technique with which to answer questions in more complicated areas, like non-equilibrium statistical physics and statistical learning. In this talk I will discuss my outlook on this topic and some interesting domains of application. I will first review what a `large deviations principle' is and why one might ever be interested in large deviations theory. I will go on to discuss a particular large deviations principle called the Freidlin--Wentzell theorem, and show how it secretly underlies a recent approach to statistical physics called stochastic thermodynamics. I will conclude with a brief discussion of how this story changes when the trajectory of a random process is coupled to some other process, and what sorts of questions that allows us to consider in physics and machine learning. 

May 18 (Room), Zoom (Recording)

Kwabena Appiah (CUNY Hunter College, Department of Mathematics and Statistics)

Undergraduate and Masters Projects Presentations

September 29 Zoom (Recording) (Slides)

Alex Ely Kossovsky (Devry College of New York)

Mathematical Perspectives in the Emergence of Physics

This presentation briefly explores humanity's first major scientific achievement, namely the discovery of modern physics during the late Renaissance era, and demonstrates the decisive role of mathematics and rudimentary data analysis in facilitating this multi-generational accomplishment. Galileo's profound insight about motion and vertical acceleration, the role of his exhaustive pendulum experiments and studies, and especially the splitting of projectile motion into its vertical accelerating component versus its horizontal inertial component as the most significant inspiration for Newton's mechanics. In addition, the inspirational history of how mathematical advances like logarithms -discovered in the early 1600s - paved the way for this remarkable scientific advance in physics shall be explored, detailing how logarithms led Kepler to the discovery of his Third Law by facilitating arithmetical computations and by hinting at power-law relationships. Kepler's planetary statistical discovery of his Third Law relates the square of the time period for one full orbit around the sun to the cube of the planet's distance from the sun, namely Period2 = K*Distance3, and this remarkable discovery was courageously based on merely six data points, corresponding to the periods and distances of the six planets known at that era. In addition, the presentation shall briefly explore the role of Newton in midwifing the birth of science with his grand synthesis of Kepler's celestial data analysis and Galileo's terrestrial experiments. Lastly, the rise and fall of Bodes' Law shall be examined, and its ambitious but failed attempt to fit the orbital distances of the planets into an exact mathematical expression shall be presented as an illustrative example of the inability to apply rigid and exact mathematical formulas to probabilistic and chanced events, such as the chaotic process of star and planet formation from the random distribution in space of gas and dust particles into much larger entities via the force of gravity. Reference book: The Birth of Science, Springer Nature Publishing. Alex Ely Kossovsky. Aug 2020. ISBN-10: 3030517438.

October 6 Zoom (Recording)

Eviatar Bach (Caltech, Division of Geological and Planetary Sciences)

Towards the combination of physical and data-driven forecasts for Earth system prediction

Due to the recent success of machine learning (ML) in many prediction problems, there is a high degree of interest in applying ML to Earth system prediction. However, because of the high dimensionality of the system, it is critical to use hybrid methods which combine data-driven models, physical models, and observations. I will present two such hybrid methods: Ensemble Oscillation Correction (EnOC) and the multi-model ensemble Kalman filter (MM-EnKF). Oscillatory modes of the climate system are one of its most predictable features, especially at intraseasonal timescales. It has previously been shown that these oscillations can be predicted well with statistical methods, often with better skill than dynamical models. However, they only represent a portion of the signal, and a method for beneficially combining them with dynamical forecasts of the full system has not previously been developed. Ensemble Oscillation Correction (EnOC) is a method which corrects oscillatory modes in ensemble forecasts from dynamical models. I will show results of EnOC applied to forecasts of South Asian monsoon rainfall, outperforming the state-of-the-art forecasts on subseasonal-to-seasonal timescales. A more general method for combining multiple models and observations is multi-model data assimilation (MM-DA). MM-DA generalizes the variational, Bayesian, and minimum variance formulation of the Kalman filter. Here, I will show how multiple model ensembles can be combined for both DA and forecasting in a flow-dependent manner using a multi-model ensemble Kalman filter (MM-EnKF). This methodology is applied to multiscale chaotic models and results in significant error reductions compared to the best model and to an unweighted multi-model ensemble. Lastly, I will discuss the prospects of using the MM-EnKF for hybrid forecasting.

October 13 Zoom (Recording)

David Newstein (Statistical and Epidemiologicial Consultant, Independent)

Insights on Bertrand's paradox from a statistician's perspective

I consider Bertrand's Paradox (1889) from the perspective of the concept of The Principle of Indifference and introduce this concept with some familiar examples. Then I give an example illustrating one of the pitfalls of applying this concept recklessly (The Hidden Cube Example). I state and give a proof of the Law of The Unconscious Statistician, which clarifies and gives a valid solution to this example. I then introduce Bertrand's Paradox and mention its historical relation to The Principle of Indifference. I proceed to derive the Probability Density Functions (PDFs) for the three cases of the Paradox utilizing another theorem (The Change of Variables Formula) which is borrowed from analysis. A proof is provided for this stochastic version of the theorem. I conduct simulations which generate the Simulated Empirical Probability Density Functions for the three cases of the Paradox, and compare them to the analytically derived PDFs, and then check their goodness of fit. I finish with a brief mention of a physicist's (E.T. Jaynes) considerations on this subject, from his paper of 1973, and examine the validity of his assertions regarding the Paradox and its relation to The Principle of Indifference.

October 20 

Hiatus

October 27 Thomas Hunter Hall, Room 412, Zoom (Recording)

Andres Contreras Murcillo (New Mexico State University, Department of Mathematical Sciences)

Orbital stability of domain walls in coupled Gross-Pitaevskii systems

In joint work with Pelinovsky and Plum, we establish an improved form of orbital stability of domain walls for a class of coupled Gross-Pitaevskii systems. We work in a suitable weighted H1-space, adapted to the domain walls to overcome the degeneracy of the linearized operator and lack of coercivity. Our proof does not make use of any integrability assumption and it is thus quite flexible. Also, our approach is strong enough to allow for controlling the modulation parameters in the time evolution of the modulation equations.

November 3 Thomas Hunter Hall, Room 412, (Recording)

Dana Ferranti (Tulane University, Department of Mathematics)

Computational Modeling of Bodies Immersed in Viscous Fluids

The Stokes equations describe fluid flows where viscous forces dominate inertial forces. These flows are relevant in the modeling of microorganism swimming, like bacteria or spermatozoa. We will give an accessible introduction to the Stokes equations, including the scaling analysis that leads to the equations and the properties which distinguish them from the broader Navier-Stokes equations. Additionally, we will discuss the method of regularized Stokeslets (MRS), a popular computational method for simulating flows generated by forces on the surfaces of bodies immersed in the fluid. The accuracy of the method relies on the choice of a blob parameter, which depends on the discretization parameter for the surface. In some applications, this dependence requires surface discretizations that are unnecessarily fine, which reduces the efficiency of the method. A modification of the MRS will be introduced which alleviates the coupling between these two parameters.

November 10 Thomas Hunter Hall, Room 412, Zoom (Slides)

Mirjeta Pasha (Tufts University, Department of Mathematics)

Modern Challenges in Large-Scale and High Dimensional Data Analysis

Rapidly growing fields such as data science, uncertainty quantification, and machine learning rely on fast and accurate methods for inverse problems. Three emerging challenges on obtaining relevant solutions to large-scale and data-intensive inverse problems are ill-posedness of the problem, large dimensionality of the parameters, and the complexity of the model constraints. Tackling the immediate challenges that arise from growing model complexities (spatiotemporal measurements) and data-intensive studies (large-scale and high-dimensional measurements collected as time-series), state-of-the-art methods can easily exceed their limits of applicability. In this talk we discuss efficient methods for computing solutions to dynamic inverse problems, where both the quantities of interest and the forward operator may change at different time instances. We consider large-scale ill-posed problems that are made more challenging by their dynamic nature and, possibly, by the limited amount of available data per measurement step. In the first part of the talk, to remedy these difficulties, we apply efficient regularization methods that enforce simultaneous regularization in space and time (such as edge enhancement at each time instant and proximity at consecutive time instants) and achieve this with low computational cost and enhanced accuracy. In the remainder of the talk, we focus on designing spatio-temporal Bayesian Besov priors for computing the MAP estimate in large-scale and dynamic inverse problems. Numerical examples from a wide range of applications, such as biomedical applications, tomographic reconstruction, image deblurring, and multichannel dynamic tomography are used to illustrate the effectiveness of the described approaches.

November 17 Thomas Hunter Hall, Room 412, Zoom (Recording)

David Goluskin (University of Victoria, Department of Mathematics and Statistics)

Studying nonlinear dynamics using computational polynomial optimization

For nonlinear ODEs and PDEs that cannot be solved exactly, various properties can be inferred by constructing functions that satisfy suitable inequalities. Although the most familiar example is proving nonlinear stability of an equilibrium by constructing Lyapunov functions, similar approaches can produce many other types of mathematical statements, including for systems with chaotic behavior. Such statements include bounds on attractor properties or on transient behavior, estimates of basins of attraction, and design of nonlinear controls. Analytical results of these types often give overly conservative results in order to remain tractable. Much stronger results can be achieved by using computational methods of polynomial optimization to construct functions that satisfy the desired inequalities. This talk will provide an overview of the different ways in which polynomial optimization can be used to study dynamics. I will show various examples in which polynomial optimization produces arbitrarily sharp results while other methods do not. I will focus on the ODE case, where theory and computational methods are more complete.

November 24 

Thanksgiving break

December 1 Thomas Hunter Hall, Room 412, Zoom (Recording)

Joshua Hudson (Sandia National Laboratories, Combustion Research Facility)

Data assimilation and inverse problems for fluid dynamics using nudging.

Nudging is a data assimilation technique where a damping term based on observational data is added to a dynamical system and acts as a corrective force on the system state. When successful, the algorithm results in convergence of the data assimilation approximation to the true solution at a much finer scale than that of the observations. In 2014, a rigorous mathematical proof was given by Azouani Olson and Titi giving conditions for the success of nudging for the 2D Navier-Stokes equations. Subsequently, similar results were obtained for several related equations. We will present some theoretical and computational results of nudging applied to the Magnetohydrodynamic equations. Then, we will discuss how nudging can be used to solve the inverse problem of inferring model parameters from the coarse state observations. We will focus on the Navier-Stokes equations with the viscosity as an unknown parameter, and discuss how and when the viscosity can be recovered. We will end with a discussion about the determining-map (the mapping of data and viscosity to a solution on the attractor), and discuss how our results extend the concept of determining modes to include the viscosity as a finitely determined quantity - this can be interpreted as a limitation on how different attractors of the Navier--Stokes (parameterized by the viscosity) can intersect.

December 8 Thomas Hunter Hall, Room 412, Zoom (Recording)

Daniel Ginsberg (Princeton University, Department of Mathematics)

Flexibility and rigidity of steady fluid motion and the distribution of heat in a fibered magnetic field

Motivated by problems in plasma physics and a conjecture of Grad, we consider some questions related to flexibility and rigidity of steady states of fluid equations. We also discuss how these problems are related to the problem of determining the distribution of heat in a strongly magnetized plasma. This addresses a recent physical conjecture of Helander, Hudson, and Paul about how the dynamical and geometric properties of the magnetic field influence heat transport. This is based on joint works with Peter Constantin, Theodore D. Drivas, and Hezekiah Grayer II.

December 15 Thomas Hunter Hall, Room 412, Zoom (Recording)

Thomas Joy and Michael Pallante (CUNY Hunter College, Department of Mathematics and Statistics)

Masters Projects Presentations

February 24  Zoom (Recording)

Aseel Farhat (Florida State University, Department of Mathematics)

A short introduction to calculus of variations and its applications 

I will give a short introduction to calculus of variations and the Euler-Lagrange equations and give some examples. I will also discuss some applications of calculus of variations in solving differential equations, such as the finite element method and the recently introduced physics-informed neural networks (PINN) algorithm. 

March 3 Zoom (Recording)

Swati Patel (Oregon State University, Department of Mathematics)

Fitting macroparasitic disease transmission models to geostatistical prevalence data

In this talk, I will discuss applying a recently developed approach to estimate parameters of a disease transmission model for a group of macroparasites that infect an estimated 1.5 billion people worldwide. While the disease is widespread, its spread occurs on relatively local scales and the vulnerability of populations can vary from region to region. Hence, key epidemiological parameters of mechanistic transmission models vary across regions and understanding these differences is important for developing strategies to mitigate morbidity of the disease. We infer these parameters for 5183 distinct regional units across sub-Saharan Africa. Inferring these parameters is challenging since data is limited to relatively few points in space and time. Previously developed geostatistical maps use this limited data, along with socioeconomic and environmental indicators, to provide broad-scale distributional estimates of disease prevalence. Using a Bayesian statistical framework that employs an adaptive multiple importance sampling algorithm, we fit these geostatistical distributional data to a transmission model. We then use these parameterized transmission models to predict how various mitigation strategies will impact broad-scale disease prevalence.

March 10  Zoom (Recording)

Julie Simons (Cal State Maritime, Department of Mathematics and Statistics)

Models for Flagellar Motion in 3D

The motion of thin structures like cilia and flagella is vital for many biological systems. In this talk, we will use reproduction and sperm motility as a primary motivator for studying the motion of flagella in 3D fluid environments. Mathematically, we can model a flagellum as a curve in space and approximate the fluid environment as a Stokesian, inertialess world. Many models for flagellar motion in such settings have been developed over the span of many decades, starting with early works using 2D approximations. More recent advancements--technologically, mathematically and computationally--have allowed for exploration of motion in fully three-dimensional contexts and some surprising results. We will describe the mathematical framework for recent work involving the Method of Regularized Stokeslets and preferred curvature and then present results involving individual swimmers near surfaces, groups of swimmers, and cooperative swimmers. We hypothesize that some species of animals have developed cellular structures that enable sperm to swim faster and more efficiently, perhaps in response to sperm competition due to mating behavior.

March 17 

Hiatus

March 24  Zoom (Recording)

Josh Hewitt (Duke University, Department of Statistical Science)

Modeling measurement and classification uncertainty in drone-based images used to estimate physical characteristics and shapes of whales

Drone-based imagery is increasingly used to measure the size and condition of marine mammals, among other species. Drones fly above a target animal, and a picture is taken. The camera's characteristics and altitude define a geometry problem that lets researchers compute the animal's size based on how big it appears in the image. But, the animal's size in the image and the altitude are observed with uncertainty. Uncertainty stems from image resolution and imperfect altimeters. Measurement errors can be estimated via a calibration study, where images are taken of references objects, whose exact length is known. We construct a hierarchical Bayesian model that uses calibration data to learn about measurement errors for several altimeters (i.e., laser-based and barometer-based), then yields posterior predictive distributions for the unknown measurements of the animals. The model's hierarchical form lets us estimate relationships between lengths and widths of whales, which is a proxy for health. We also estimate uncertainty for length-based estimates of a whale's maturity, and discuss extending the model to other animals, imaging problems, and measured quantities and relationships.

March 31 

Hiatus

April 7 Zoom (Recording)

Isabel Scherl (University of Washington, Department of Mechanical Engineering)

Experimental Fluid Mechanics with Machine Learning

The ability to understand unsteady fluid flows is foundational to advancing technologies across fields. We use cutting edge data-driven methods (i.e. machine learning) to interpret and control unsteady fluid flows through experiments in the following three cases: 1. We use robust principal component analysis (RPCA) to improve flow-field data by leveraging global coherent structures to identify and replace spurious data points. In all cases, both simulated and experimental, we find that RPCA filtering extracts dominant coherent structures and identifies and fills in incorrect or missing measurements. 2. We optimize a two cross-flow (i.e. vertical-axis) turbine array using a hardware-in-the-loop approach and find that arrays with well-considered geometries and control strategies can outperform isolated turbines by up to 30%. 3. Using similar turbines, we create an experimental framework to more efficiently explore arrays' high-dimensional parameter space. Our data-driven approach allows us to model parameter spaces using sparse data. As a result, we are able to map turbine system dynamics with orders of magnitude fewer data points.

April 14  Zoom (Recording)

Le Mai Nguyen Weakley (Indiana University, High Performance Computing)

High Performance Computing by a Mathematician

Since the emergence of distributed systems and cluster computing capable of doing large scale parallel calculations, High Performance Computing (HPC) has been a cornerstone in scientific discoveries that require large scale simulations like weather and climate forecasting, astronomy, QCD, among a variety other disciplines that require such workflows. In today's data-driven world and with the introduction of hardware that allow for faster matrix operations, HPC has become a tool for researchers and machine-learning enthusiasts everywhere. This talk will give an overview of HPC and how the author went from pursuing their doctorate in mathematics to a career in High Performance Computing.

April 21 

Spring Break

April 28  Zoom (Recording)

Zachary Simon (Lockheed Martin, Autonomy and Artificial Intelligence)

(Cancelled)

May 5 

Hiatus

May 12  Zoom (Recording)

Caihua Chen, Yanlin Ou, Keven Calderon, Fardous Sabnur, Yana Mross (CUNY Hunter College)

Masters Projects Presentations

Please join us to support the presentations of your peers.

September 30  Zoom (Recording)

Sushovan Mahji (UC Berkeley, School of Information)

A Taste of Topological Data Analysis (TDA): Reconstruction of Shapes

Topological data analysis (TDA) is a growing field of study that helps address data analysis questions. TDA is deemed a better alternative to traditional statistical approaches when the data inherit a topological and geometric structure. Most of the modern technologies at our service rely on geometric shapes in some way or the other, be it the Google Maps showing you the fastest route to your destination or the 3D printer on your desk creating an exact replica of a relic---shapes are being repeatedly sampled, reconstructed, and compared by intelligent machines. In this talk, we will catch a glimpse of how some of the famous topological concepts---like persistent homology, Vietoris-Rips and Cech complexes, Nerve Lemma, etc---lend themselves well to the reconstruction of shapes from a noisy sample.

October 7  Zoom (Recording)

Yassin Chandran (CUNY Graduate Center, Department of Mathematics)

Automorphisms of the k-curve graph

Our main objective is to study symmetry groups of surfaces which are called mapping class groups. To any surface, we can construct a graph whose vertices correspond to certain equivalence classes of simple closed curves and whose edges are drawn whenever the associated curves can be realized disjointly. These graphs are known as curve graphs. Nikolai Ivanov showed that the automorphism group of the curve graph is exactly the mapping class group of the surface, which led him to propose the following meta-conjecture: Any sufficiently rich graph associated to a surface must have the same symmetry group as the surface. In this talk, we'll discuss a large class of graphs, known as k-curve graphs, associated to the surface, for which Ivanov's meta-conjecture holds true. This is joint work with S. Agrawal, T. Aougab, M. Loving, J. R. Oakley, R. Shapiro, and Y. Xiao.

October 14 Zoom (Recording)

Stephen W. Morris (University of Toronto, Department of Physics)

Consider the Icicle

Icicles are harmless and picturesque winter phenomena, familiar to anyone who lives in a cold climate. The shape of an icicle emerges from a subtle feedback between ice formation, which is controlled by the release of latent heat, and the flow of water over the evolving shape. The water flow, in turn, determines how the heat flows. The air around the icicle is also flowing, and all forms of heat transfer are active in the air. Ideal icicles are predicted to have a universal "platonic" shape, independent of growing conditions. In addition, many natural icicles exhibit a ripply shape, which is the result of a morphological instability. The wavelength of the ripples is also remarkably independent of the growing conditions. Similar shape and ripple phenomena are also observed on stalactites, although certain details of their formation differ. We built a laboratory icicle growing machine to explore icicle physics. We learned what it takes to make a platonic icicle and the surprising origin of the ripples.

October 21 Zoom (Recording)

Vincent Martinez (CUNY Hunter, Department of Mathematics and Statistics)

Parameter estimation for nonlinear dynamical systems

An inherent problem in the modeling of natural phenomena is in obtaining accurate estimation of the parameters in the system. For instance, when studying fluid motion, the Navier-Stokes equations provides a model for a viscous, incompressible fluid flow in the form of a partial differential equation for the velocity of the fluid. The material parameter in this system is the fluid's kinematic viscosity. Typically, the value of this parameter is determined empirically by experiments or statistically by data, and its exact value depends on the particular fluid itself. This poses the following fundamental mathematical question: Is it possible to recover the true value of the viscosity by having only partial information about the motion of the velocity itself? In other words, under what scenarios is it mathematically possible for one to recover this unknown viscosity? In this talk, we discuss a dynamic algorithm that allows one to learn the true values of parameters in certain nonlinear dynamical systems as partial observations are made on the system.

October 28  Zoom (Recording)

Nga Yu Lo (Macaulay Honors College at Hunter, Mathematics and Computer Science Major)

Evaluating Object Recognition Behavioral Consistency on Out-of-Distribution Stimuli

State-of-the-art artificial neural networks (ANN) trained on ImageNet are known for their top performance on object recognition tasks. They are the best model of the primate ventral stream with moderate success at explaining neural activities as well as visual behavior. To an ANN trained on object recognition, an out-of-distribution (o.o.d.) stimulus is an image with features that differs drastically from the train dataset and usually reduces a model's object recognition performance. Geirhos et al (2020) shows that models are little above chance at predicting human behavior on o.o.d. stimuli. With a dataset consisting of 16 categories and 3 o.o.d. domains, they measure agreement between model and human responses at a visual classification task, using a word association to extract behavioral choices from Imagenet trained models. We find, however, that using an image-level discriminability metric (Rajalingham, Issa et al, 2018) and training a logistic regression model, ANNs have a higher behavior consistency than reported in Geirhos et al. With different ANN models varying in human behavior consistency, these results imply the need to integrate multiple behavioral benchmarks in a unified manner to enable comparisons of models of the human ventral stream. This is joint work with Tiago Marques and James DiCarlo at M.I.T.

November 4 Zoom (Recording)

Yuan Pei (Western Washington University, Department of Mathematics)

Velocity-vorticity-Voigt model for PDEs in fluid dynamics

In this talk, we propose the so-called velocity-vorticity-Voigt (VVV) model for the Navier-Stokes system as well as the the Boussinesq equations, both in three dimension. We briefly introduce the two fundamental models in fluid dynamics, and the Voigt regularization. Then, we outline the back- ground and motivation of the model. In our work, we add a Voigt regularization term only to the momentum equation in velocity-vorticity formu- lation without regularizing the vorticity. We prove global well-posedness and regularity of this model along with an energy identity. We also show convergence of the model's velocity and vorticity to their counterparts in the 3D Navier-Stokes equations as the Voigt modeling parameter tends to zero. Similar discussion will be given for the Boussinesq system with thermal fluctuation. Part of the work is jointly with Adam Larios at University of Nebraska-Lincoln and Leo Rebholz at Clemson University.

November 11  Zoom (Recording)

Sathyanarayanan Chandramouli (Florida State University, Department of Mathematics)

Theoretical characterization of viscous conduit breathers

The spatio-temporal evolution of the circular interface between two miscible fluids of high viscosity contrast (a viscous conduit) has proven to be an ideal platform for studying nonlinear dispersive hydrodynamic (DH) excitations. The two-fluid dynamics in the bulk is essentially described by a Stokes flow, while the conduit interface is effectively non-dissipative, thanks to extremely slow rates of mass diffusion. We investigate the existence and characterization of envelope solitary waves (breather solutions) of the conduit equation, a long wavelength, fully nonlinear PDE model of conduit interfacial dynamics. Bright and dark breathers represent a class of fundamental multi-scale, propagating DH excitations. Bright breathers have been obtained numerically and investigated across the entire range of nonlinearity. We propose a three-parameter characterization of these solutions, with a counterintuitive, continuous deformation into the dark breathers across the zero-dispersion line. The talk will highlight the novelties of the numerical scheme used to compute conduit breathers, the identification of universal frameworks to study such solutions, and future applications in internal oceanic waves.

November 18, 25 (Seminar Break)

December 2,  Zoom (Recording)

Evelyn Lunasin (United States Naval Academy, Department of Mathematics)

Optimal mixing and optimal stirring for fixed energy, fixed power, or fixed palenstrophy flows

Optimal stirring for transient mixing is a particularly timely problem and the ability to investigate optimized flows computationally yields both intuitive insights into effective stirring strategies and allows testing of the a priori analysis. The thrust of studies in this direction will be toward determining sharp estimates on the rate of mixing (in terms of the H-1 mix-norm) and understanding qualitative and quantitative properties of flows that realize those absolute limits. We consider passive scalar mixing by a prescribed divergence-free velocity vector field in a periodic box and address the following question: Starting from a given initial inhomogeneous distribution of passive tracers, and given a certain energy budget, power budget, or finite palenstrophy budget, what incompressible flow field best mixes the scalarquantity? We present explicit example demonstrating finite-time perfect mixing when there is finite energy constraint on the stirring flow. On the other hand, we show that finite-time perfect mixing is ruled out in the case of finite palenstrophy. Finally, we show how theorems of transportation distances and rearrangement costs be linked into sharp results for the H-1 mix-norm with power-constrained flows. This is joint with Zhi Lin, Alexei Novikov, Anna Mazzucato, and Charlie R. Doering

December 9,  Zoom (Recording)

Yu-Min Chung (Research Scientist, Eli Lilly and Company)

My transition from academia to industry

''Math can do anything'' is a famous quote from one of IBM ads. It is inspiring but I didn't quite understand it when I was a graduate student. I have spent most of my life in academia from a college student to a tenure-track professor studying and researching mathematics, in particular, the applied mathematics. During the time in academia, it is fascinating to witness how mathematics can be applied in other scientific fields. To further explore more possibilities, recently, I have switched my role from a math professor to a research scientist in a pharmaceutical company. In this forum, I wish to share my personal experiences in both academia and industry such as their differences/similarities, interview processes, expectations, and the math that we use. Any questions you may have are particularly welcome. 

December 16  Zoom (Recording)

Tom Fleming (Quantitative Analyst, Finance Sector)

Ill-posed problems and too many tools: A case study in applied mathematics

An applied mathematician often works as a subject matter expert within a broader business organization. As a result, their work can resemble that of a technical consultant; non-technical people realize they have a problem that would benefit from quantitative modeling or analysis, but aren't sure how to frame or even fully describe the problem. It is up to the applied mathematician to not only find or develop techniques to solve the problem, but to figure out what exactly needs to be solved. We will walk through an example from the speaker's experience in finance that demonstrates the difficulty in discovering what the problem actually is, as well as the challenges in choosing among possible techniques for solving it.

February 25, 2021, Zoom (Recording)

Florian Mudekereza (Hunter Applied Math MA student, Adviser: Dana Sylvan)

Stochastic Statistical Inference in Games with Noisy Data

This talk concerns the development of a stochastic model for environments where players (producers) use statistical inference to form beliefs and make decisions. In the proposed setup, producers act as statisticians, each one obtains small noisy samples of the market supply, uses stochastic algorithms to improve their estimate of the market supply, and chooses to best-respond to this estimate. The proposed model relaxes the usual bounded rationality assumption by allowing producers to be aware of the noise and randomness in their data and stochastic estimates. As a result, this approach generates two key predictions which depend crucially on the sample size: asymptotically (i.e., in large samples), the stochastic estimates are shown to converge to the sampling equilibrium with statistical inference (SESI) market supply, Q_SESI; in small samples, there is a smaller market supply due to the low confidence level producers have in their stochastic estimates which leads to the proposed equilibrium concept called stochastic SESI (SSESI) Q_SSESI. Monte Carlo simulations illustrate the convergence of Q_SSESI to Q_SESI while their mean squared error is shown to be of order O(1/n). Potential improvements of this rate are explored.

March 4, 2021, Zoom (Recording)

Elizabeth Carlson (University of Nebraska-Lincoln)

Accurately Modeling Fluid Flow: Data Assimilation, Parameter Recovery, & Ocean Modeling

Scientists and mathematicians apply the continuum hypothesis to model fluid flow, i.e. the flow of substances like air or water. One of the challenges of the accurate simulation of turbulent flows is that initial data is often incomplete. Data assimilation circumvents this issue by continually incorporating the observed data into the model. In this talk, I will discuss my work using a new approach to data assimilation in order to both accurately model fluid flow and to identify certain physical properties of the fluid being modeled. I will also discuss implementation of this algorithm in large-scale climate models.

March 11, 2021, Zoom (Recording)

Owen Kunhardt (Hunter College Computer Science/Math BA student)

The Effects of Image Distribution and Task on Adversarial Robustness

Currently, few studies testing the theories of adversarial robustness take into consideration that when doing comparisons across each dataset, both the image distributions (e.g. digits vs objects) and classification task (to classify digits vs objects) are different. To unravel the causal factors of the inherent adversarial robustness of a model, we propose an unbiased metric to compare adversarial robustness and perform a series of experiments. In these experiments, we equalized several training hyperparameters on networks for the MNIST and CIFAR-10 datasets to determine whether the image distribution and task played a role in adversarial robustness. We find that networks trained for digit classification on MNIST digits are more adversarially robust than networks trained to do object classification on CIFAR-10 objects. In addition, to pin-point whether the contribution of adversarial robustness is mainly due to the image distribution or the task, we create a fusion image dataset that overlapped MNIST digits with CIFAR-10 objects such that image statistics were matched and train networks to perform a digit or object classification task. We find that models performing digit recognition on the fusion images were more robust than those performing object recognition, empirically verifying the role of the classification task in the adversarial robustness of a model, independent of the image distribution a network is trained on. Comparing the fusion model performances to their non-fusion counter-parts, we find that image distribution also plays a role.

March 18, 2021, Zoom (Recording)

Seckin Demirbas (University of British Columbia-Vancouver)

A Study on Certain Periodic Schrodinger Equations

This will be an informal introductory talk on the periodic cubic Schrodinger equation on 2-D irrational tori and the cubic fractional Schrodinger equation on the torus. We will discuss different tools and methods and how they ensure the local and/or global well-posedness of solutions to the equations at hand. We will also discuss the Sobolev norm growth for the global solutions of the periodic cubic Schrodinger equation on 2-D irrational tori.

March 25, 2021, Zoom (Recording)

Keisha Cook (Tulane University)

Single Particle Tracking with Applications to Lysosome Transport

Live cell imaging and single particle tracking techniques have become increasingly popular amongst the mathematical biology community. We study endocytosis, the cellular internalization and transport of bioparticles. This transport is carried out in membrane-bound vesicles through the use of motor proteins. Lysosomes, known for endocytosis, phagocytic destruction, and autophagy, move about the cell along microtubules. Single particle tracking methods utilize stochastic models to simulate intracellular transport and give rise to rigorous analysis of the resulting properties, specifically related to transitioning between inactive to active states. This confidence in the stochastic modeling of particle tracking is useful not only for particle-containing lysosomes, but also broad questions of cellular transport studied with single particle tracking.

April 8, 2021, Zoom

Greg Lyng (Optum Labs, UnitedHealth Group)

A year of COVID-19 models at OptumLabs

In this talk, we give a high-level (and selective) overview of the role that mathematical modeling has played in the OptumLabs response to the COVID-19 pandemic. This portfolio of models includes both national scale models of the spread of disease and local models aimed at informing surveillance testing and school/business reopening. 

April 15, 2021, Zoom (Recording)

Pooja Rao (MSRI at UC Berkeley)

A novel strategy for unstructured search on IBM quantum processors

Grover's search is one of the most important quantum computing algorithms for unstructured search. However, when implemented on a real quantum device, the corresponding circuit depth increases prohibitively as the search domain gets bigger. A long circuit is undesirable as it leads to more quantum noise, which leads to poor results. In this talk, we introduce the basics of our algorithmic approach - based on quantum partial search - that reduces the depth of the quantum circuits significantly. With this approach, we have been able to design state-of-the-art circuits that not only show significant improvements over other existing results, but go a step further in being able to search through a bigger database.

April 22, 2021, Zoom (Recording)

Emmanuel Asante-Asamani (Clarkson University)

A mathematical model of weight change in humans

Weight management is of great concern to many Americans. People are either trying to lose weight or gain weight for health or aesthetic reasons. Often this endeavor is successful in the short term but fails in the long term. The question on the minds of most weight watchers is how to maintain the weight they have worked so hard to lose. Recently, a hormone secreted in the adipose tissues of mammals (leptin) was discovered and found to act on critical brain regions to control food intake and energy expenditure. Its primary goal is to maintain the body's fat stores. In this talk, I will present an extension of a mathematical model of weight dynamics to include the activity of leptin. The model explains why maintaining lost weight is so difficult and provides critical insight into how weight change can be maintained long term. 

April 29, 2021 (Re-scheduled to Fall semester, September 23, 2021), Zoom

Aseel Farhat (Florida State University)

(TBA)

May 6, 2021, Zoom (Recording)

David Sondak (Harvard University)

Towards Bridging Machine Learning and Physics

A primary goal of science is to develop predictive models of physical phenomena. This is extraordinarily challenging, especially when multiscale physics is involved. Over the years, research has focused on trying to unlock the secrets of the governing equations as well as developing reduced models that capture the physical essence while being quick and easy to use. Recent research thrusts have started to bring machine learning algorithms to bear on classical physical problems such as fluid turbulence. This talk will provide an overview of an overview of neural networks and how they have been applied to physical problems. New results will be presented on an autoencoder neural network with a sparsity promoting latent space applied to canonical nonlinear partial differential equations.

May 13, 2021, Zoom

Cooper Boniece (Washington University in St. Louis)

A new stochastic process with multivariate covariance self-similarity

Stochastic processes that display aspects of scale invariance -- i.e., that possess features that remain unchanged under appropriate rescaling -- have been applied in a wide variety of disciplines ranging from hydrology to telecommunications to finance. However, by comparison to univariate models, far less attention has been paid to characteristically multivariate scale invariance models that display behavior that the limit theory arguably suggests is most natural. In this talk, I will discuss some mathematical background on scale invariant stochastic processes and some interesting aspects of a new family of processes called operator fractional Lévy motion. This is related to joint work with Gustavo Didier (Tulane University).

October 1, 2020, Zoom

Yu-Min Chung (University of North Carolina-Greensboro)

What is the shape of your data? An Introduction to Topological Data Analysis and its Application to Data Sciences

Topological Data Analysis is a relatively young field in algebraic topology. Tools from computational topology, in particular persistent homology, have proven successful in many scientific disciplines. Persistence diagrams, a typical way to study persistent homology, contain fruitful information about the underlying objects. Extracting features from persistence diagrams is one of the major research areas in this field. In this talk, we will give a brief introduction to persistent homology, and we will demonstrate methods we propose to summarize persistence diagrams. Applications to various datasets from cell biology, medical imaging, physiology, and climatology, will be presented to illustrate the methods. This talk is designed for a general audience in mathematics. No prior knowledge in algebraic topology is required.

October 8, 2020, Zoom

Luan Hoang (Texas Tech University)

Long-time asymptotic expansions for viscous incompressible fluid flows

We study the long-time dynamics of viscous incompressible fluids for both Eulerian and Lagrangian descriptions. For the Eulerian description, a solution of the Navier-Stokes equations with a potential or time-decaying body force admits a Foias-Saut asymptotic expansion as time tends to infinity. This expansion provides very precise asymptotic approximations of the solution in terms of polynomial and exponential functions. For the Lagrangian description, we prove that the trajectories of the fluid particles also have similar asymptotic expansions. This is established by studying the system of nonlinear ordinary differential equations relating the Lagrangian trajectories to the solutions of the Navier-Stokes equations.

October 15, 2020, Zoom (Recording)

Tural Sadigov (Hamilton College)

Support Vector Machines: Overview and Applications

In this talk, we review the main idea behind statistical (machine) learning and focus on binary classification. We define the problem of classification and introduce the maximal margin classifier, support vector classifier, and, eventually, support vector machines. We formulate optimization problems for the maximization of the margin and apply the algorithms to simulated and real datasets.

October 22, 2020, Zoom

Deniz Bilman (University of Cincinnati)

What do Riemann-Hilbert problems tell us about nonlinear waves?

Riemann-Hilbert problems provide a powerful analytical tool to study various problems in pure and applied mathematics. In particular, they provide analogues of integral representations for solutions of integrable nonlinear wave equations (e.g. the Korteweg-de Vries equation), from which we can extract detailed information about the wave field with the aid of nonlinear asymptotic analysis methods. This framework leads also to a powerful method for numerical solution of the Cauchy problem. In this talk, I will describe the role of Riemann-Hilbert problems in studying solutions of nonlinear wave equations and discuss recent results obtained using this approach. One example will be on formation of rogue waves, which are large disturbances of the sea surface that appear out of nowhere and disappear just as suddenly.

October 29, 2020, Zoom (Recording)

Angeline Aguinaldo (University of Maryland-College Park)

Category Theory for Software Modeling and Design

This talk will discuss category theory and its potential applications to software modeling. Category theory provides a convenient algebraic system for encoding processes and their composition. This may be useful in precisely and intuitively characterizing the modularity and interoperability of software programs and systems. This talk will discuss an application of category theory to robot manipulator programming. 

November 5, 2020, Zoom

Pawan Patel (Millenium Management)

Covariance Estimators, Portfolio Theory, and RMT

Estimation of true covariance matrices in real world predictive modelling is one of the key challenges to accurate modelling. It's importance arises in a range of real world applications: from election modelling, to numerous applications in Machine Learning prediction, and even Portfolio Theory for stock trading. In this talk we'll review the basics of covariance matrices and their importance in portfolio theory. We'll discuss some common methods for covariance estimation and where Random Matrix Theory can help. 

November 12, 2020, Zoom

Victor Ginting (University of Wyoming-Laramie)

A Petrov-Galerkin FEM for solving second-order IVP and its a posteriori error estimation

We present a Petrov-Galerkin FEM for solving second-order IVPs from which a class of time integration schemes can be derived. Several standard techniques can also be recovered from this variational setting. The key in the derivation is the choice of finite element spaces and the numerical integration techniques utilized to calculate the functional in the variational equation. We discuss an adjoint-based a posteriori error estimate of the approximation. Several numerical examples are given to illustrate the performance of the resulting schemes and the corresponding error estimate.

November 19, 2020, Zoom (Recording)

Jeungeun Park (University of Cincinnati)

Collective behavior in bacterial chemotaxis

The preferred movement of a bacterium along the gradient of chemical substances is called chemotaxis. Bacterial chemotaxis has been widely studied from both the microscopic and macroscopic points of view; in particular, it is important to connect these different levels of description to understand better a realistic model of bacterial chemotaxis. In this talk, we analyze the collective motion of a population of Escherichia coli bacteria in response to multiple external stimuli by incorporating the signaling machinery of individual cells. Motivated by some experiments from the literature, we consider two chemical stimuli and show that the collective motion of bacteria depends on the ratio of their corresponding chemoreceptors. Furthermore, we examine our theory with Monte-Carlo agent-based simulations, which qualitatively captures the experimental observation from the literature. This is joint work with Zahra Aminzare.

December 3, 2020, Zoom (Recording) (Audio Transcript)

Jared Berman (Spark Foundry, Applied Math MA Alum 2019, Adviser: Vincent Martinez)

Efficient Model Building with Python

When building a machine learning model for predictions, a part of the canonical workflow is to try out many combinations of data pre-processing transformations on different models and hyperparameter sets for which, with the objective of shortlisting the best combinations. Luckily we don't have to reinvent the wheel to accomplish this. Scikit-learn provides utilities to automate the trying-out process. Moreover, the interfaces follow a clean API very closely, making the code logic very easy to follow, and therefore making the code very practical. I've found that this greatly enhances the model building process by reducing the amount of time spent on tedium. 

December 10, 2020, Zoom

Kenneth Brown (Hunter College, Applied Math MA Thesis, Adviser: Vincent Martinez)

Higher-order synchronization for a data assimilation algorithm with nodal value observables

The analytical study of a nudging algorithm in the infinite-dimensional setting of PDEs was initially carried out by Azouani, Olson, and Titi for the two-dimensional (2D) incompressible Navier-Stokes equations (NSE). In their seminal work, convergence of the approximating solution to the true solution was shown to take place at least in the topology of the Sobolev space H1 . However, their analysis did not treat uniform convergence or higher-order Sobolev spaces. This talk will discuss convergence in stronger Sobolev topologies, including the uniform topology, of this nudging based algorithm for data assimilation in the context of the 2D NSE when observations of the flow are given as nodal values of the velocity field.

February 13, 2020, GC Room 6496

Mimi Dai (University of Illinois-Chicago)

Wild solutions for MHD models

We will discuss some wild behaviors exhibited by weak solutions of the magnetohydrodynamics with Hall effect and one of its limit cases. It includes lack of uniqueness of weak solutions in the Leray-Hopf class and construction of finite energy weak solutions that do not conserve magnetic helicity and magnetic energy.

February 20, 2020, HE 930

Cecilia Mondaini (Drexel University)

Rates of convergence to statistical equilibrium: a general approach and applications

This talk focuses on the study of convergence/mixing rates for stochastic dynamical systems towards statistical equilibrium. Our approach uses the weak Harris theorem combined with a generalized coupling technique to obtain such rates for infinite-dimensional stochastic systems in a suitable Wasserstein distance. In particular, we show two scenarios where this approach is applied in the context of stochastic fluid flows. First, to show that Markov kernels constructed from a suitable numerical discretization of the 2D stochastic Navier-Stokes equations converge towards the invariant measure of the continuous system. This depends crucially on a spectral gap result for the discrete Markov kernel that is independent of the level of discretization. Second, to approximate the posterior measure obtained via a Bayesian approach to inverse PDE problems, particularly when applied to advection-diffusion type PDEs. In this latter case, the Markov transition kernel is constructed with an exact preconditioned Hamiltonian Monte Carlo algorithm in infinite dimensions. A rigorous proof of mixing rates for such algorithm was an open problem until quite recently. Our approach provides an alternative and flexible methodology to establish mixing rates for other Markov Chain Monte Carlo algorithms. This is a joint work with Nathan Glatt-Holtz (Tulane U).

March 19, 2020, Zoom

Na Cai (Hunter Applied Math MA student, Adviser: Emmanuel Asante-Asamani)

An Exponential Time Differencing-Real Distinct Poles Scheme for Solving Reaction Diffusion Equations

We focus on solving a non-homogeneous ordinary differential equation with initial conditions. First, we find a one-step solution using the Exponential Time Differencing (ETD) Scheme. Then we use the Real Distinct Poles (RDP) Scheme to deal with the exponential part of the solution. This results in the ETD-RDP Scheme, which provides low computational cost for solving ODEs without sacrificing efficiency.

April 23, 2020, Zoom

Michael Barile (Yardi Systems, Applied Math MA Alum 2019, Adviser: John Loustau and Emmanuel Asante-Asamani)

RealTech for Investment Management

The presenter will discuss working at Yardi Systems, a leading property management software company, in the Investment Management department. He will present an overview of the core functionality of the IM module, and describe the basic features that clients typically use to automate accounting activity, track transactions and measure investment performance. Additionally, he will discuss where skills developed in studying math have been useful in the workplace, as well as related areas that math students intending to work in the Fin/RealTech industries should spend some time developing before graduation. 

April 30, 2020, Zoom

Padi Fuster Aguilera (Tulane University)

A PDE model for chemotaxis with logistic growth

Chemotaxis is the movement of an organism in response to a chemical stimulus and is a fundamental mechanism of motion for many organisms in nature. In this talk we will explain how chemotaxis can be modeled as a partial differential equation (PDE), as well as announce some recent results for a Keller-Segel-type chemotaxis model that accounts for logistic growth. This is joint work with Vincent Martinez and Kun Zhao. 

May 7, 2020, Zoom

Michael Y. Levy (St. John's University)

Dependence Structure of Hyperball Distribution

The purpose of this seminar is to describe the dependence structure of a multivariate joint distribution obtained from a Cartesian product of finitely many hyperballs of a given dimension. The method I use to obtain the dependence structure is to apply Sklar’s theorem. The results include the explicit calculation univariate marginal cumulative distribution functions of certain random variables and its copula, which links the random variables. The copula of the hyperball distribution is interpreted within the context of the unique independence copula. The univariate marginal cumulative distribution functions of the hyperball distribution is a transcendental equation interpreted within the context of classical and quantum mechanics. The univariate marginal distribution functions of the hyperball distribution relates to Kepler’s equation. I interpret my results by comparing the trajectories that I observe in the philosophy of political thought with the trajectories that I observe in celestial mechanics and quantum mechanics. I assert that because of the inherent indeterminism and uncertainty in political systems, the dynamics will behave more similarly to quantum systems and statistical systems than celestial systems. While this seminar offers a complicated description of independent random variables distributed on a hyperball; I anticipate that making these results patent in this manner will allow for the application of Sklars theorem on more complicated product manifolds.

May 14, 2020, Zoom

Say Park (Hunter Applied Math MA student, Adviser: Emmanuel Asante-Asamani)

The role of cell geometry in steady-state bleb size and shape

Dictyostelium discoideum is a soil-living amoeba which can move by making pressure driven protrusions of its plasma membrane, referred to as blebs. This eukaryotic microbe is a model organism for biomedical research as its fundamental cellular processes and molecular genetic pathways are similar to cells linked to human disease and cancer cells. We study specifically its motility in response to a chemoattractant (chemotaxis), as the process is an essential early event in metastasis of cancer cells. Chemotaxing cells are typically polarized, adopting a plethora of non-symmetric morphologies. Yet, not much is known about the influence of local cell geometry on the steady-state size and shape of blebs. Existing mathematical models of bleb expansion use prototypical spherical geometries to represent the cell boundary, thus easing the burden of numerical computations. As a result, the simulated bleb expansion process is insensitive to membrane curvature. In this work, we develop a curvature dependent mathematical model to predict terminal bleb size via a variational approach. We demonstrate for the first time the use of B-splines in discretizing the resulting functional, thereby simplifying its application to realistic cell geometries. Our model reproduces known effects of membrane tension, linker tension and hydrostatic pressure on terminal bleb size. The model along with data obtained from D.discoideum cells show that blebs are dependent on local cell geometry and preferentially terminate in negative curvature regions. 

May 21, 2020, Zoom

Paul Popa (Hunter Applied Math MA student, Adviser: Vincent Martinez)

Conditioned Ensemble Kalman Filters for Data Assimilation with Noisy Observations

The Lorenz equations of 1963, originally derived as a simplified model of atmosphere dynamics, are a classical example of a chaotic dynamical system. Assuming that the true state of our system is given by the Lorenz equations, we seek to improve forecasts on its future state, given noisy, partial observations at the current time by leveraging apriori knowledge about the true state. In particular, we modify the Ensemble Kalman Filter (EnKF) conditioned to this apriori knowledge in three different ways. Numerical studies are carried out to test whether or not these modifications increase the accuracy of forecasts relative to the standard EnKF algorithm. The results of the studies are presented.

April 3, 2019

Alina Vdovina, Mathematics, Newcastle University, UK

Title: Higher-Dimensional Expanders with Applications to Clustering

Wednesday, April 3, 2019 in Room 921 East Building, 1:10-2:00 pm  (GRECS Seminar)

Abstract: We will present explicit constructions of ramanujan graphs and ramanujan complexes, and discuss how extremal spectral properties can be used for optimal cuts of various data sets.

Alina Vdovina was the Ada Peluso Visiting Professor of Mathematics at Hunter College for Fall 2017 and Spring 2018. She has published 40 papers in a broad range of fields: geometry and analysis on groups acting on buildings, graph theory, construction of new algebraic varieties, geometry of Riemann surfaces, knot theory, constructing C*- algebras and computing their K-theory, non-commutative geometry and operator theory, geometric and combinatorial group theory. Professor Vdovina was an invited speaker at over 20 international conferences and gave over 60 invited research seminar and colloquia talks, invitations for thematic programs at the Max-Planck-Institute, Bonn, Cambridge, Berkeley, ETH Zurich, IHES and Institute Henri Poincare Paris. She received the Lise Meitner award (Germany) in 2002. Some of her ongoing international collaborations include the “Harvard Picture Language Project”. She is a trustee of the London Mathematical Society, a member of the LMS Research Grants Committee, and a Fellow of Higher Education Academy (UK).

May 1, 2019

Vincent Guirardel, University of Rennes, France

Title: Surface Groups in Germs of Analytic Diffeomorphisms in One Variable

Wednesday, May 1, 2019 in Room 920 East Building, 1:10-2:00 pm  (GRECS Seminar)

Abstract: Consider the group G of germs of analytic diffeomorphisms at the origin in the complex plane C, i.e. of power series in one variable with positive radius of convergence and with non-zero derivative at 0 (the group law being composition).  For instance, given a codimension-one foliation of a complex manifold and a leaf L of this foliation, the holonomy along L gives morphism from the fundamental group of L to G.  We prove that the group G contains subgroups isomorphic to the fundamental group of any closed orientable surface, thus answering a question by Ghys.  This is a joint work with Cantat, Cerveau and Souto.

Professor Vincent Guirardel is a leading expert in geometric group theory, geometric topology and dynamics.  He has authored numerous papers published in the “Duke Mathematica Journal”, “Commentarii Mathematici Helvetici”, “Mathematische Annalen”, “Geometry and Topology”, “Journal of Topology”, “Memoirs of the American Mathematical Society”, “Asterisque”, and other prestigious publication venues.  He is a current editor of “The Annalen de la Faculte des Sciences de Toulouse” and of the “Annalen Henri Lebesque”.  Since 2016 he also serves as the Director of the Center Henri Lebesque in Rennes.  He is also a member of the Institut Universitaire de France.

Constrained Factor Models for High-Dimensional Matrix-Variate Time Series

Friday, February 23, 2018 in Room 920 East Building, 12 noon-1:00 pm

Presented by Elynn Chen, Statistics PhD Candidate, Rutgers University

Abstract: High-dimensional matrix-variate time series data are becoming widely available in many scientific fields, such as economics, biology, and meteorology.  To achieve significant dimension reduction while preserving the intrinsic matrix structure and temporal dynamics in such data, Wang et al. 2017 proposed a matrix factor model that is shown to provide effective analysis. In this paper, we establish a general framework for incorporating domain or prior knowledge in the matrix factor model through linear constraints. The proposed framework is shown to be useful in achieving parsimonious parameterization, facilitating interpretation of the latent matrix factor, and identifying specific factors of interest. Fully utilizing the prior-knowledge-induced constraints results in more efficient and accurate modeling, inference, dimension reduction as well as a clear and better interpretation of the results.  In this paper, constrained, multi-term, and partially constrained factor models for matrix-variate time series are developed, with efficient estimation procedures and their asymptotic properties. We show that the convergence rates of the constrained factor loading matrices are much faster than those of the conventional matrix factor analysis under many situations.  Simulation studies are carried out to demonstrate the finite-sample performance of the proposed method and its associated asymptotic properties. We illustrate the proposed model with three applications, where the constrained matrix-factor models outperform their unconstrained counterparts in the power of variance explanation under the out-of-sample 10-fold cross-validation setting.

Robust Nonparametric Functional Data Analysis Based on Depth

Friday, March 2, 2018 in Room 920 East Building, 12 noon-1:00 pm

Presented by Sara Lopez-Pintado, Professor of Statistics, Columbia University

Abstract: Technological development in many emerging research fields has led to the acquisition of large collections of data of extraordinary complexity.   In neuroscience for example, brain-imaging technology has provided us with complex collections of signals from individuals in different neurophysiological states in healthy and diseased populations. These signals can be collected and represented as functions. The development of statistical tools to analyze this type of high-dimensional data set is very much needed. I will present new robust methodologies for analyzing functional and imaging data based on the concept of depth.  Functional depth provides a rigorous way of ranking a sample of functions from center-outward. This ordering allows us to define robust descriptive statistics such as medians, trimmed means and central regions for functional data. Moreover, data depth is often used as a building block for developing robust statistical methods and outlier-detection techniques. Permutation and global envelope depth-based tests for comparing the locations of two groups of functions or images are proposed and calibrated. The performances of these methods are illustrated in simulated and real data sets.  In particular, we tested differences between PET (Positron Emission Tomography) brain images of healthy controls and patients with severe depression.  We also used these methods to test differences between the growth pattern of normal and low birth weight children.

Methods and Software Development for Interval-Censored Time-to-Event Data

Friday, March 9, 2018 in Room 920 East Building, 12 noon-1:00 pm

Presented by Chun Pan, Clinical Biostatistician, Novartis Oncology

Abstract: Interval-censored time-to-event data occur naturally in studies of diseases where the symptoms of interest are not directly observable, and periodic laboratory or clinical examinations are required for detection. Due to the lack of well- established procedures, interval-censored data have been conventionally treated as right-censored data; however, this introduces bias at the first place. This presentation gives an overview of my current research, which focuses on methodological research and software development for analyzing interval- censored data. Specifically, it will present the three research projects that have been completed. The first project is a Bayesian semiparametric proportional hazards model with spatial random effect for spatially correlated interval- censored data. In the second project, we developed a multiple frailty proportional hazards model with frailty selection for clustered interval-censored data, which is analogous to a mixed model in regression analysis. In the third project, we created an R package “ICBayes” for regression analysis and survival curve estimation of interval-censored data based on several published papers by our research team. At the end, this presentation will lay out some directions for future research.

Algorithmic problems for quasiconvex subgroups of hyperbolic groups

Tuesday, April 24, 2018 in Room 920 East Building, 3:00-4:00 pm  (GRECS Seminar)

Presented by Eric Swenson, Professor of Mathematics, Brigham Young University

Abstract: We discuss algorithms for determining whether a quasiconvex subgroup is almost malnormal and an algorithm for determining the numbers of ends of the pair for a quasiconvex subgroup.

Consensus Estimates of Precipitation from Diverse Data Sources in High Mountain Asia

Wednesday, September 26, 2018 in Room 921 East Building, 2:00-2:30 pm

Presented by William F. Christensen, Chair of Statistics, Brigham Young University

Abstract: With the exception of the earth’s polar regions, the High Mountain Asia region (including the Tibetan Plateau) contains more of the world’s perennial glaciers than any other.  Sometimes called the third pole because of its massive storage of ice, High Mountain Asia (HMA) provides water to one-fifth of the world’s population.  Due to changes in precipitation patterns and temperatures warming faster in HMA than the global average, the region faces increased risk of flooding, crop damage, mudslides, economic instability, and long-term water shortages for the communities down-river.  In this talk, we discuss a large, interdisciplinary, multi-institutional research project for characterizing climate change in HMA.  We illustrate the use of latent variable models for extracting consensus estimates of spatiotemporally-correlated climate processes from a suite of climate model outputs and remote-sensing observations, and we discuss the uncertainty quantification needed to inform probability-based decision making.  We conclude with a discussion of decision making, uncertainty, and the important role of statisticians in framing the public debate about climate change abatement.

An Invitation to Wikipedia Editing

Wednesday, October 17, 2018 in Room 920 East Building, 1:10-2:00 pm  (Department Colloquium)

Presented by Prof. Ilya Kapovich, Department of Mathematics & Statistics, Hunter College, CUNY

Abstract: Wikipedia has become an indispensable resource that millions of people use every day as a source of knowledge and information. Yet surprisingly few academics, including scientists and mathematicians, regularly (or ever) edit Wikipedia. In this talk I will discuss the basics of becoming a Wikipedia editor, including the main rules, policies and differences in culture with the academic world.  I will also show how to edit Wikipedia on mathematical/scientific topics, both in terms of modifying existing Wikipedia articles and creating new ones. We will conclude with a live demo of posting a brand new math article to Wikipedia. This talk is intended for a broad audience and no specific expertise in mathematics is required.

Fibres of Failure: Diagnosing Predictive Models Using Mapper

Thursday, October 18, 2018 in the Hemmerdinger Screening Room, 7th Fl Library, 5:30-6:30 pm  (Department Colloquium)

Presented by Prof. Mikael Veldemo-Johansson, Department of Mathematics, College of Staten Island, CUNY

Abstract: The Mapper algorithm is able to produce intrinsic topological models of arbitrary data in high dimensions.  Through a statistical adaptation of the Nerve lemma, the algorithm can be seen to reproduce the topology and parts of the geometry of the data source under assumptions of dense sampling and good parameter choices.  In this talk, we will describe how by careful choice of the Mapper model parameters, the resulting topological model can be guaranteed to separate input values to the predictive process for prediction error, grouping high-error and low-error regions separately.  This approach produces a diagnostic process where local failure modes can be classified, feeding into either a model development process or a local correction term to improve predictive performance.  We have successfully applied this approach to temperature prediction in steel furnaces.

Understanding outer automorphisms of free groups using geodesics in Culler-Vogtmann outer space

Friday, November 9, 2018 in Room 921 East Building, 1:00-2:00 pm  (GRECS Seminar)

Presented by Catherine Pfaff, Asst. Professor of Mathematics, Queen’s University at Kingston, Ontario, Canada

Abstract: Outer space was defined by Culler and Vogtmann in 1986 as a simplicial complex (minus certain faces) on which the outer automorphism group of the free group would act nicely as a symmetry group.  Through later developments, representatives of many of these outer automorphisms as geodesics were determined.  In this talk I will introduce outer space, these geodesics, and several ways in which we’ve used them to understand outer automorphisms of free groups.

About the Speaker: Catherine Pfaff is a tenure-track Assistant Professor of Mathematics at the Queen’s University at Kingston in Ontario, Canada. She received a PhD in Mathematics from Rutgers University at New Brunswick in 2012, and has held postdoctoral and visiting positions at the Aix-Marseille University, at the University of Bielefeld, and at the University of California at Santa-Barbara. Catherine’s research concentrates on the study of algebraic, probabilistic, dynamical and geometric properties of free group automorphisms.

The primitivity index function for a free group, and untangling closed geodesics on hyperbolic surfaces

Wednesday, February 22, 2017 in Room 920 East Building, 1:10-2:10 pm  (GRECS Seminar)

Presented by Ilya Kapovich, the Ada Peluso Visiting Professor, Hunter College; Professor of Mathematics, University of Illinois at Urbana-Champaign

Abstract: An important result of Scott from 1980s shows that every closed geodesic on a compact hyperbolic surface can be lifted (or “untangled”) to a simple closed geodesic in some finite cover of that surface.  Recent work of Patel and others initiated quantitative study of Scott’s result, which involves understanding the smallest degree of a cover where a closed geodesic “untangles”, compared with the length of the curve.

Motivated by these results of Scott and Patel, we introduce several “untangling” indexes for nontrivial elements of a finite rank free group F, such as the “primitivity index”, the “simplicity index” and the “non-filling index”.  We obtain several results about the worst-case behavior of the corresponding index functions and about the probabilistic behavior of the indexes on “random” elements of F.

We also discuss applications of these results to the original setting of Scott and Patel of untangling closed geodesics on hyperbolic surfaces.

The talk is based on a joint paper with Neha Gupta, with an appendix by Khalid Bou-Rabee.

Groups and Semigroups with Applications to Computer Science

Wednesday, March 1, 2017 in Room 920 East Building, 1:10-2:10 pm (GRECS Seminar)

Algebraic Rigidity and Randomness in Geometric Group Theory

Presented by Ilya Kapovich, the Ada Peluso Visiting Professor, Hunter College; Professor of Mathematics, University of Illinois at Urbana-Champaign

Abstract: Counting particular mathematical structures up to an isomorphism is an important basic mathematical problem.   In many instances, e.g. for counting graphs and finite groups (with various restrictions), good precise or asymptotic counting results are known.   However, until recently very little has been known about counting isomorphism types of finitely presented groups, with various restrictions on the size and the type of a group presentation.   The reason is that, by a classic result of Novikov and Boone, the isomorphism problem for finitely presented groups is algorithmically undecidable.   Even for those classes of groups where the isomorphism problem is decidable, the known algorithms are usually too complicated to help with counting problems.

In this talk we will survey recent progress in this direction, based on joint work with Paul Schupp.  The key results, allowing for asymptotic counting of isomorphism types, involve establishing several kinds of algebraic rigidity properties for groups given by “generic” presentations.  A representative result here is an isomorphism rigidity theorem for generic one-relator groups. As an application, we compute the precise aymptotics of the number of isomorphism classes of one-relator groups as the length of the defining relator tends to infinity.

Groups as geometric objects

Wednesday, March 15, 2017 in Room 921 East Building, 12:15-1:05 pm  (GRECS Seminar)

Presented by Ilya Kapovich, the Ada Peluso Visiting Professor, Hunter College; Professor of Mathematics, University of Illinois at Urbana-Champaign

Abstract: We will give a broad survey of geometric group theory, an active area of mathematics which emerged as a distinct subject in early 1990s and which is located at the juncture of group theory, differential geometry, and geometric topology.  We will discuss the various questions, tools and ideas from geometric group theory, as well as some open problems.  The talk does not assume any prior knowledge of the subject and should be accessible to general audience.

Semi-parametric dynamic factor models for non-stationary time series

Wednesday, March 22, 2017 in Room 922 East Building, 12:15-1:05 pm  (CUNY Applied Probability & Statistics Seminar)

Presented by Giovanni Motta, Pontificia Universidad Catolica de Chile

Abstract: A novel dynamic factor model is introduced for multivariate non-stationary time series. In a previous work, we have developed asymptotic theory for a fully non-parametric approach based on the principal components of the estimated time-varying covariance and spectral matrices. This approach allows both common and idiosyncratic components to be non-stationary in time. However, a fully non-parametric specification of covariances and spectra requires the estimation of high-dimensional time-changing matrices. In particular when the factors are loaded dynamically, the non-parametric approach delivers time-varying filters that are two-sided and high-dimensional. Moreover, the estimation of the time-varying spectral matrix strongly depends on the chosen bandwidths for smoothing over frequency and time. As an alternative, we propose a new approach in which the non-stationarity in the model is due to the low-dimensional latent factors. We distinguish between the (double asymptotic) framework where the dimension of the panel is large, and the case where the cross-section dimension is finite. For both scenarios we provide identification conditions, estimation theory, simulation results and applications to real data.

Interpreting variation across trials in neurophysiology

Wednesday, March 29, 2017 in Room 922 East Building, 1:15-2:25 pm  (CUNY Applied Probability & Statistics Seminar)

Presented by Asohan Amarasingham, Associate Professor, Department of Mathematics, City College of  New York

Abstract: How do neurons code information, and communicate with one another via synapses? Experimental approaches to these questions are challenging because the spike outputs of a neuronal population are influenced by a vast array of factors. Such factors span all levels of description, but only a small fraction of these can be measured, or are even understood. As a consequence, it is not clear to what degree variations in unknown and uncontrolled variables alternately reveal or confound the underlying signals that observed spikes are presumed to encode. A related consequence is that these uncertainties also disturb our comfort with common models of statistical repeatability in neurophysiological signal analysis. I will describe these issues to contextualize tools developed to interpret large-scale electrophysiology recordings in behaving animals, focusing on conceptual issues. Applications will be suggested to the problems of synaptic and network identification in behavioral conditions as well as neural coding studies.?

Growth of finitely presented Rees quotients of free inverse semigroups

Wednesday, April 19, 2017 in Room 920 East Building, 1:10-2:10 pm  (GRECS Seminar)

Presented by Professor David Easdown, School of Mathematics and Statistics at the University of Sydney, Australia

Abstract: Inverse semigroups are an abstraction of collections of partial one-one mappings of a set closed under composition and inversion.  Free inverse semigroups exist, and resemble free groups, except that in the usual reduction of words, one “remembers” detail about the cancellations that have taken place, captured precisely using concatenation and reduction of Munn trees. Free inverse semigroups possess ideals, factoring out by which yields Rees quotients, which are also inverse semigroups, now with zero.  When everything is finitely generated, we have usual notions of growth.  Idempotents proliferate when working with inverse semigroup presentations with zero, introducing subtleties and requiring new techniques compared with group or semigroup presentations.  Growth of finitely presented Rees quotients of free inverse semigroups turns out to be polynomial or exponential, and algorithmically recognizable, using modifications of graphical constructions due to De Bruijn, Ufnarovsky, Gilman, and can also be understood with respect to criteria involving height, in the sense of Shirshov.  Polynomial growth is coincidental with satisfiability of semigroup identities, in particular related to Adjan’s identity for the bicyclic semigroup. The boundary between polynomial and exponential growth is also interesting with regard to the notion of deficiency of the presentation, yielding concise sharp lower bounds for polynomial growth, and classifications of classes of semigroups where the lower bounds are achieved.

This is joint work with Lev Shneerson, Hunter College of CUNY.

Expander Graphs From Buildings

Wednesday, October 11, 2017 in Room 920 East Building, 1:15 pm  (Department Colloquium)

Presented by Alina Vdovina, the Ada Peluso Visiting Professor, Hunter College; Lecturer Pure Mathematics, Newcastle University, United Kingdom

Abstract: Expander graphs are one of the deepest tools of several branches of mathematics and theoretical computer science, appearing in all sorts of contexts since their introduction in the 1970s.  Expander graphs are graphs which are sparse and highly connected in the same time.  We will cover our construction of the first examples of Cayley graph expanders of groups defined explicitly by generators and relations.

Alina Vdovina (Newcastle University, UK) is the Ada Peluso Visiting Professor of Mathematics at Hunter College for Fall 2017 and Spring 2018. She has published 35 research articles in a broad range of fields: geometry and analysis on groups acting on buildings, graph theory, construction of new algebraic varieties, geometry of Riemann surfaces, knot theory, constructing C*- algebras and computing their K-theory, non-commutative geometry and operator theory, geometric and combinatorial group theory, cryptography. Professor Vdovina was an invited speaker at over 20 International conferences and gave over 60 invited research seminar and colloquia talks, including lectures for thematic programs at the Max-Planck-Institute (Bonn), Cambridge, Berkeley, ETH (Zurich), IHES and Institute Henri Poincare (Paris). She received the Lise Meitner award (Germany) in 2002. Some of her ongoing international collaborations include the “Harvard Picture Language Project”. She is a trustee of the London Mathematical Society, a member of the LMS Research Grants Committee, and a Fellow of Higher Education Academy (UK).

Ring Theoretic Analogues of C*-Algebras

Wednesday, October 25, 2017 in Room 921 East Building, 1:10-2:10 pm  (GRECS Seminar)

Presented by Ben Steinberg, Professor of Mathematics, City College of New York, CUNY

Abstract: Many C*-algebras have purely algebraic analogues over an arbitrary base commutative ring. For example, group C*-algebras correspond to group rings. Over the past decade there has been a lot of work on the ring theoretic analogue of Cuntz-Krieger (or graph) C*-algebras, called Leavitt path algebras. There are a number of interesting commonalities between graph C*-algebras and Leavitt path algebras, such as they both have the same criteria for simplicity, primitivity and they both have the same K_0-groups. The proofs however have been entirely different in the analytic and algebraic contexts.

Most of the C*-algebras are examples of groupoid algebras.   I recently introduced a ring theoretic analogue of groupoid C*-algebras. The close relations between the C*-algebras and their algebraic counterparts are usually explained by the groupoid. Many other interesting C*-algebras now have purely algebraic versions that are quite natural. Nekrashevych has use groupoid algebras to construct simple algebras of quadratic growth over fields of any characteristic, answering a question of Jason Bell.

In this talk we’ll survey some examples, results and open questions.

Classifying Amalgams

Wednesday, November 1, 2017 in Room 921 East Building, 1:10-2:14 pm  (GRECS Seminar)

Presented by Corneliu Hoffman, University of Birmingham, UK

Abstract: We discuss the problem of classifying amalgams that look like the amalgam of small rank Levi subgroups in groups of Kac-Moody type (and some interesting subgroups). It turns out that, under very mild assumptions, these either collapse or are isomorphic to a standard amalgam of a twisted form of the corresponding group of Kac-Moody type. This is a result that is needed in the second generation proof of the Classification of Finite Simple Groups.

About the Speaker: Corneliu Hoffman obtained his PhD in 1998 from the University of Southern California. Prior to moving to Birmingham held academic positions at the University of California Irvine, and The Mathematical Research Institute in Berkeley and Bowling Green State University in the US. His research interests include various kinds of Group Theory as well as some topics in Computer Assisted Proofs.

Wicks forms and normal forms for the mapping class group of a once punctured surfaces
Friday, November 17, 2017 in Room 5417 CUNY Graduate Center, 4:00-5:00 pm  (NY Group Seminar and GRECS Seminar)

Presented jointly by Eric Swenson, Professor of Mathematics, Brigham Young University, and Alina Vdovina, the Ada Peluso Visiting Professor, Hunter College

Abstract: Mosher obtains a automatic structure on the mapping class group of a once punctured surface of genus $g$ using ideal “triangulations” of the surface. We translate this into the setting of wicks forms of genus $g$ of maximal length, which I think of as a connected cubic graph $\Gamma$ on 4g-2 vertices with specified orientable circuit. Let $v$ be the vertex corresponding to $\Gamma$ in the Mosher complex $Y$. Any other vertex $w$ of $Y$ is uniquely represented as a finite sequence of paths (without backtracking) in $\Gamma$. Any edge path in $Y$ from $v$ to $w$ is realized as a sequence of elementary moves on $Y$ (each of which takes a path without backtracking to a path without backtracking). These moves will change each of the given paths into an empty path.

Analysis of Error Control in Large Scale Two-Stage Multiple Hypothesis Testing

Wednesday, November 29, 2017 in Room 921 East Building, 1:15-2:15 pm  (CUNY Applied Probability and Statistics Seminar)

Presented by Wenge Guo, Associate Professor of Statistics, New Jersey Institute of Technology

Abstract: When dealing with the problem of simultaneously testing a large number of null hypotheses, a natural testing strategy is to first reduce the number of tested hypotheses by doing screening or selection, and then to simultaneously test selected hypotheses. The main advantage of this strategy is to greatly reduce the severe effect of high dimensions. However, the first screening or selection stage must be properly accounted for in order to maintain some type of error control. In this talk, we will introduce a selection rule based on the selection statistic which is independent of the test statistic when the tested hypothesis is true. Combining this selection rule and the conventional Bonferroni procedure, we can develop a powerful and valid two-stage procedure. The suggested procedure has several nice properties: (i) completely remove the selection effect; (ii) reduce the multiplicity effect; (iii) do not waste any samples while carrying out both selection and testing. Asymptotic power analysis and simulation studies illustrate that this proposed method provides higher power compared to usual multiple testing methods while controlling the type 1 error rate. Optimal selection thresholds are also derived based on our asymptotic analysis. This is a joint work with Joseph Romano from Stanford University.

Infinite Periodic Groups and Burnside Problems

Wednesday, December 13, 2017 in Room 921 East Building, 3:00-4:00 pm  (GRECS Seminar)
Presented by Diljit Singh, Mathematics Major at Hunter College

Abstract: We will talk about different formulations of Burnside’s problems and list major milestones towards the 1994 result by Zelmanov. We will sketch a short proof of the Golod and Shafarevich theorem and the construction of a counterexample to the General Burnside Problem.

Synchronizing finite automata: a problem everyone can understand but nobody can solve (so far)

Wednesday, February 17, 2016 in Room 920 East Building, 1:00-2:00 pm  (Departmental Lecture Series)

Presented by Mikhail Volkov, Ada Peluso Visiting Professor, Hunter College; Professor of Mathematics, Ural Federal University, Russia

Abstract: Most current mathematical research, since the 60s, is devoted to fancy situations: it brings solutions which nobody understands to questions nobody asked” (quoted from Bernard Beauzamy, “Real Life Mathematics”, Irish Math. Soc. Bull. 48 (2002), 43-46).  This provocative claim is certainly exaggerated but it does reflect a really serious problem: a communication barrier between mathematics (and exact science in general) and human common sense.  The barrier results in a paradox: while the achievements of modern mathematics are widely used in many crucial aspects of everyday life, people tend to believe that today mathematicians do “abstract nonsense” of no use at all.  In most cases it is indeed very difficult to explain to a non-mathematician what mathematicians work with and how their results can be applied in practice.  Fortunately, there are some lucky exceptions, and one of them has been chosen as the present talk’s topic.  It is devoted to a mathematical problem that was frequently asked by both theoreticians and practitioners in many areas of science and engineering.  The problem, usually referred to as the synchronization problem, can be roughly described as the task of determining the simplest way to restore control over a device whose current state is not known:– think of a satellite which loops around the Moon and cannot be controlled from the Earth while “behind” the Moon.  While easy to understand and practically important, the synchronization problem turns out to be surprisingly hard to solve even for finite automata that constitute the simplest mathematical model of real-world devices.  This combination of transparency, usefulness and unexpected hardness should, hopefully, make the talk interesting for a wide audience.

Professor Volkov will also give a semester course on synchronizing automata (Synchronizing Finite Automata: Math 795.64. Th, 7:35-9:25 pm, Room 921 East). The course is basically self-contained as it requires almost no prerequisites; in particular, no prior knowledge of automata theory is assumed. The course contains a detailed overview of the current state-of-the-art in the theory of synchronizing automata and quickly leads to some recent advances of the theory and a number of tantalizing open problems.

Road Coloring Theorem

Wednesday, February 24, 2016 in Room 920 East Building, 1:00-2:00 pm  (GRECS Seminar)

Presented by Mikhail Volkov, Ada Peluso Visiting Professor, Hunter College; Professor of Mathematics, Ural Federal University, Russia

Abstract: I shall present a recent advance in the theory of finite automata: Avraam Trahtman’s proof of the so-called Road Coloring Conjecture by Adler, Goodwyn, and Weiss; the conjecture that admits a formulation in terms of recreational mathematics arose in symbolic dynamics and has important implications in coding theory.  The proof is elementary in its essence but clever and enjoyable.

Matrix Identities Involving Multiplication And Transposition

Wednesday, April 20, 2016 in Room 920 East Building, 1:30-2:30 pm  (GRECS Seminar)

Presented by Mikhail Volkov, Ada Peluso Visiting Professor, Hunter College; Professor of Mathematics, Ural Federal University, Russia

Abstract: Matrices and matrix operations constitute basic tools for algebra, analysis and many other parts of mathematics.  Important properties of matrix operations are often expressed in form of laws or identities such as the associative law for multiplication of matrices.  Studying matrix identities that involve multiplication and addition is a classic research direction motivated by several important problems in geometry and algebra.  Matrix identities involving along with multiplication and addition also certain involution operations (such as taking the usual or symplectic transpose of a matrix) have attracted much attention as well.

If one aims to classify matrix identities of a certain type, then a natural approach is to look for a collection of “basic” identities such that all other identities would follow from these basic identities.  Such a collection is usually referred to as a basis.  For instance, all identities of matrices over an infinite field involving multiplication only are known to follow from the associative law.  Thus, the associative law forms a basis of such “multiplicative” identities.  For identities of matrices over a finite field or a field of characteristic 0 involving both multiplication and addition, the powerful results by Kruse–L’vov and Kemer ensure the existence of a finite basis.  In contrast, multiplicative identities of matrices over a finite field admit no finite basis.

Here we consider matrix identities involving multiplication and one or two natural one-place operations such as taking various transposes or Moore–Penrose inversion.  Our results may be summarized as follows.

None of the following sets of matrix identities admits a finite basis:

• the identities of n×n-matrices over a finite field involving multiplication and usual transposition;

• the identities of 2n×2n-matrices over a finite field involving multiplication and symplectic transposition;

• the identities of 2×2-matrices over the field of complex numbers involving either multiplication and Moore–Penrose inversion or multiplication, Moore–Penrose inversion and Hermitian conjugation;

Algebra in Automata Theory

Wednesday, September 28, 2016 in Room 920 East Building, 1:15 pm  (GRECS Seminar)

Presented by Pascal Weil, the Ada Peluso Visiting Professor, Hunter College; Research Professor, National Centre for Scientific Research, Université Bordeaux, France

Abstract: Automata and formal language theory are cornerstones of theoretical computer science with a strong mathematical flavor.  The basic concepts include finite state automata and regular languages.  Automata are a natural tool to represent and work on regular languages.  Another important tool for specifying regular languages is provided by logic (first order and monadic second order).  Logic is a great specification tool, but it does not have good algorithmic properties, and this is where algebra comes into play.  With every finite state automaton, we can associate a finite algebraic structure, namely a monoid whose algebraic properties reflect the combinatorial or logical properties of the language accepted by the automaton.  The fact that this so-called syntactic monoid is finite and effectively constructible gives us an elegant tool to effectively decide certain properties of regular languages.

Pascal Weil is a Research Professor of the highest rank in the National Centre for Scientific Research.  Professor Weil received a Doctorate degree in Informatics from the University of Paris-7 in 1985, a PhD in Mathematics from the University of Nebraska- Lincoln in 1988, and a Habilitation Degree in Informatics from the University of Paris-6 in 1989.  He was director of LaBRI (Bordeaux Research Lab in Computer Science) from 2011 to 2015, as well as the Chair of the Scientific Council for Information Sciences (a national council within CNRS) from 2010 to 2014.  Professor Weil has over 80 publications (including over 50 journal articles) focused on algebraic methods in computer science, notably in the field of automata and formal language theory and algorithmic and combinatorial problems in group theory.

Wednesday, October 19, 2016 in Room 922 East Building, 1:15-2:05 pm

The 2016 Nobel for the Economics of Contracts: A Primer on Contract Design Modeling as a Problem of Statistical Inference with Applications in Financial Contracting

Presented by Jonathan Conning, Associate Professor, Department of Economics, Hunter College and the CUNY Graduate Center

Abstract: The 2016 Nobel Prize in Economics has just been awarded to Oliver Hart and Bengt Holmstrom “for their contributions to contract theory.”  This talk will provide a short primer on some of the main modeling ideas in the field of field contract design under asymmetric information, with an emphasis on financial contracting under moral hazard. Holmstrom’s (1979) paper on Moral Hazard and Observability and Grossman and Hart’s (1983) paper An Analysis of the Principal-Agent Problem established the modern “state space” approach to the problem which allowed the field to flourish and explode.  In the canonical single-task moral hazard contracting problem a Principal (e.g. landowner, firm owner, investor) wishes to enter into a contract with an Agent (e.g. worker-cum-tenant, employee, entreprenneur/borrower) to carry out a task or project whose stochastic outcome can be described by a statistical distribution which that can be shifted by the agent’s choice of action (e.g. the agent’s diligence or effort).  When both the project’s outcomes and the agent’s action choices are both observable and contractible this is just a standard neo-classical problem (e.g. financial contracts with Arrow-Debreu state-contingent commodities and standard asset pricing formulas).  When the agent’s actions are not observable the contract design problem becomes a statistical inference and constrained optimization problem: how to design a contract that ties the agent’s renumeration to observable outcomes that strikes a balance between providing incentives for the agent to choose a right level of unobserved diligence/effort without imposing too much costly risk.  After establishing a few key results of the canonical case the presentation moves on to study more challenging and interesting contracting situations from Holmstrom’s work (and this author’s own work) to study multi-task and multi-agent principal agent problems.  I discuss questions such as the possible uses of relative-performance evaluation (tournaments), whether to organize contracting directly through bilateral contracts or via specialized intermediaries of joint-liability structures and other topics and show how the framework is helpful for analyzing key questions in modern corporate finance such as how firms borrow (via bonds, bank debt or equity), the design of microfinance contracts for the (collateral) poor, questions of regulation, the optimal size of banks and ownership structure of banks and much else.

First-Order Definable Languages and Counter-Free Automata

Wednesday, November 16, 2016 in Room 920 East Building, 1:10-2:10 pm  (GRECS Seminar)

Presented by Pascal Weil, the Ada Peluso Visiting Professor, Hunter College; Research Professor, National Centre for Scientific Research, Université Bordeaux, France

Abstract: We will discuss the deep connections between automata theory, formal language theory and logic.  Regular languages (those that are accepted by finite state automata) are known to be exactly those specified by monadic second order logic (MSO).  First-order logic is a very natural fragment of MSO: it is natural to ask whether that fragment is sufficient to specify regular languages (it isn’t!), and to characterize first-order definable languages.  The theorems of Schützenberger and McNaughton-Papert give a nice solution to this problem, with characterizations in terms of automata theory and in terms of regular expressions.  It is however a third characterization, of an algebraic nature (it uses the notion of the syntactic monoid of a language: a finite, effectively computable monoid attached to a regular language), which provides the tools to effectively decide first-order definability.

Quantifier alternation defines a natural hierarchy within first order logic, which yields an infinite hierarchy of within the class of first-order definable languages.  Investigating the decidability of this hierarchy is a challenging and active research area.  Only a few of the lower levels of this hierarchy are known to be decidable.

Pascal Weil is a Research Professor of the highest rank in the National Centre for Scientific Research.  Professor Weil received a Doctorate degree in Informatics from the University of Paris-7 in 1985, a PhD in Mathematics from the University of Nebraska- Lincoln in 1988, and a Habilitation Degree in Informatics from the University of Paris-6 in 1989.  He was director of LaBRI (Bordeaux Research Lab in Computer Science) from 2011 to 2015, as well as the Chair of the Scientific Council for Information Sciences (a national council within CNRS) from 2010 to 2014.  Professor Weil has over 80 publications (including over 50 journal articles) focused on algebraic methods in computer science, notably in the field of automata and formal language theory and algorithmic and combinatorial problems in group theory.

The research theme for the academic year 2014-2015 will be the subject of hyperbolic geometry and its many related areas.  The year will feature a series of lectures, an ongoing seminar, and several visitors. 

During this period the Ada Peluso Visiting Professors will be

•  Athanase Papadopoulos of the Universite de Strasbourg (Fall 2014).

• Hugo Parlier of the University of Fribourg, Switzerland (Spring 2015).

The first two seminars will be given by Ara Basmajian and the next four by Athanase Papadopoulos.

Taxicabs and the Sum of Two Cubes

Tuesday, March 12, 2013 in Room 714 West Building, 5:30 pm. (Fourth Distinguished Undergraduate RTG Lecture in Number Theory, a Joint Project of Columbia University, CUNY, and New York University) 

Presented by Joseph H. Silverman.

Abstract: Some numbers, such as 9=13+23 and 370=33+73, can be written as the sum of two cubes.  Are there numbers that can be written as the sum of cubes in two (or more) essentially different ways?  This elementary question will lead us into beautiful areas of mathematics where number theory, geometry, algebra, calculus, and even internet security interact in surprising ways.

Using Geometry To Classify Surfaces

Wednesday, March 7, 2012 in 224 East Building, 1:10-2:30 pm (Soup and Science Series)

Presented by Ara Basmajian, Professor of Mathematics, Hunter College and the Graduate Center of the City University of New York.

Abstract: We will begin with the question: What properties do the surface of a basketball and the surface of a football share? In what sense are they the same? In what sense are they different? This discussion will lead naturally to the notion of a surface (a two dimensional space). Next, we introduce the three basic geometries (euclidean, spherical, hyperbolic) and their properties. Hyperbolic geometry, though the least known of the three, plays a prominent, fundamental role in our understanding of surfaces and the geometries they admit. In fact, we will see that most surfaces admit a hyperbolic geometry. We will finish by mentioning some recent work on three dimensional spaces.

On Motions-Continuous, Quasiconformal, and Holomorphic

Wednesday, March 14, 2012 in Room 920 East Building, 3:00-4:00 pm (Departmental Lecture Series)

Presented by Sudeb Mitra, Queens College and the Graduate Center of the City University of New York.

Abstract: The idea of holomorphic motions was first introduced by Mane, Sad, and Sullivan, in their study of the dynamics of rational maps. Since then, it has found important applica- tions in many branches of complex analysis and dynamics. An important topic is the question of extending holomorphic motions. In this talk, we will relate that question to contin- uous motions and quasiconformal motions (in the sense of Sullivan and Thurston). We will also give simple examples of holomorphic motions of a finite set over the punctured unit disk, that cannot be extended to the Riemann sphere. If time permits, we will discuss an application in geometric function theory. All basic definitions and motivations will be given.

Overgroup Lattices in Finite Groups

Wednesday, October 24, 2012 in Room 920 East Building, 1:30-2:30 pm, preceded by a Tea at 1:00 pm (Departmental Lecture Series)

Presented by Levi Biock, BA/MA student in Mathematics, Hunter College of the City University of New York.

Abstract: To answer the Palfy-Pudlak Question, John Shareshian conjectured that a certain class, Dd, of lattices are not overgroup lattices in any finite group.  To prove this conjecture one needs to know the structure of a group G and the embedding of a subgroup H in G, such that there are only two maximal overgroups of H in G and H is maximal in both.  Towards a proof of this conjecture, we consider the minimal normal subgroups of G and use these minimal normal subgroups to determine the structure of G and determine the embedding of H in G.

This work was carried out at SURF 2012, California Institute of Technology, mentor: Michael Aschbacher.

A Knot’s Tale For Halloween

Wednesday, November 7, 2012 in Room 920 East Building, 1:10-3:00 pm.  Lunch and refreshments served following the talk.  (Soup and Science Series)

Presented by Tatyana Khodorovskiy, Assistant Professor of Mathematics, Hunter College of the City University of New York.

Abstract: Knots have appeared many times in human history, from marine knots to Celtic knots to our own knotted up DNA! As a mathematical subject, knot theory began in 1867, when Lord Kelvin was working on creating the periodic table of elements.  He proposed that the different chemical properties of atoms can be described by the different ways their tubes of ether are knotted up.  He and physicist Peter Tait went on to compose the first table of knots. Well, this particular connection didn’t really pan out so well…  Today, however, knot theory is an indispensable part of a field of math called topology.  In this talk, I will define what knots are and discuss their role in life and math.

A Quick Trip Through Clifford Algebras

Wednesday, March 9, 2011 in Room 920 East Building, 3:00-4:00 pm (Departmental Colloquium)

Presented by Martin Bendersky, Professor of Mathematics, Hunter College and the City University of New York Graduate Center

Abstract: Clifford algebras appear in myriad topics in mathematics. For example, they appear in Diracs quantization of the electron, the theory of elliptic operators (in particular, the Dirac operators) and the study of division algebras. I will focus on their application to constructing vector fields on spheres. The prerequisite is Linear Algebra. The word Tensor will appear in the talk.

Hochschild Complexes and Mapping Spaces

Wednesday, April 13, 2011 in Room 920 East Building, 3:00-4:00 pm (Departmental Colloquium)

Presented by Mahmoud Zeinalian, Long Island University

Abstract: Free loop spaces, or more generally spaces of maps from one manifold into another, appear in many branches of mathematics including topology, analysis, differential geometry, quantum field and string theories.  In this talk, I will explain, from an elementary view point, how some important geometric objects on these mapping spaces are described in terms of familiar and tractable data on their domains and targets.  I will discuss how some rather sophisticated algebraic objects, such as the Hochschild complexes, and the higher dimensional analogues, have their roots in elementary calculus calculations.

Adding and Counting

Tuesday, March 8, 2010 in Room 510 North Building, 5:45 PM (Second Distinguished Undergraduate RTG Lecture in Number Theory, a Joint Project of Columbia University, CUNY, and New York University)

Presented by Ken Ono, Professor of Mathematics, Emory University / University of Wisconsin, Madison

Abstract: In mathematics, the stuff of partitions seems like mere child’s play. The speaker will explain how the simple task of adding and counting has fascinated many of the world’s leading mathematicians: Euler, Ramanu- jan, Hardy, Rademacher, Dyson, to name a few. And as is typical in number theory, many of the most fundamental (and simple to state) questions have remained open. In 2010 the speaker, with the support of the American Institute for Mathematics and the National Science Foundation, assembled an international team of distinguished researchers to attack some of these problems. Come hear Professor Ono speak about their findings: new theories which solve some of the famous old questions.

The function n -> n!

Tuesday, April 27, 2010 in Room 714 West Building, 4:00-5:00 PM (First Distinguished Undergraduate RTG Lecture in Number Theory, a Joint Project of Columbia University, CUNY, and New York University)

Presented by Benedict Gross, Professor of Mathematics, Harvard University

Abstract: I will first consider the size of n! when n is large,proving an estimatethat was obtained by de Moivre in the early 18th century. I will then define Euler’s gamma function, which is a beautiful extension of the function n! to the real numbers, and will discuss some results on its values at rational numbers. Finally, I will introduce p-adic numbers, and study a p-adic analog of the gamma function. It’s values at rational numbers bear a striking resemblance to the values in the real case.

Unexpected Phenomena in High Dimensions

Wednesday, April 28, 2010 in Room 920 East Building, 1:00-2:00 pm (Departmental Colloquium)

Presented by Paul Goodey, Professor of Mathematics and Chair, University of Oklahoma

Abstract: We will discuss a number of geometric phenomena which occur only in high dimensions. These will primarily comprise a mixture of geometry and analysis although some will be purely combinatorial.

Romberg Integration Using the Midpoint Formula

Wednesday, November  3, 2010 in Room 920 East Building, 1:10-2:00 pm (Departmental Colloquium)

Presented by Roger Pinkham, Professor Emeritus, Stevens Institute of Technology and Visiting Professor at Hunter College, CUNY

Abstract: An oft used technique of numerical integration bears the name Romberg. Romberg integration is the shrewd application of a general idea known as Richardson’s method of “extrapolation to the limit”. It involves repeated application of the trapezoidal rule and allows for repeated re-use of previous function evaluations. Now the midpoint rule uses half the function evaluations and has an error term half that of the trapezoidal rule. As a result, I wondered whether an analog of Romberg integration could be based on the midpoint rule. In this talk I show that it can.

Computer Graphics and the Geometry of Complex Polynomials

Wednesday, February 25, 2009 in Room 920 East Building, 1:10-2:00 pm (Departmental Lecture Series)

Presented by Linda Keen, Professor of Mathematics, Lehman College and Graduate Center, CUNY

Abstract: The last thirty years have seen incredible developments in understanding the field of “dynamical systems” and there is every indication that it will continue to be a gold mine for mathematics for many more years to come. One way into the theory is to take a family of functions, like the family qa(x) = ax(1 – x) of quadratic polynomials, and to apply them repeatedly to a particular value of x. For example, as a varies, is there any difference in how the sequence  x0 = 1/2,  x1 = qa(x0),  x2= qa(x1),…, xn = qa(xn-1 ),…  behave? What if we fix a and vary the starting point X0 away from 1/2? Already in these simple cases, we will see there are interesting things to say, and if we allow complex numbers as the values for a and x, rather than just real values, some truly fascinating and beautiful geometry emerges. The famous Mandelbrot set arises from this example. We will see why, and we will see how computer-generated patterns can get our intuition primed to create new mathematics.

The Discrete Charms of Topology

Wednesday, March 18, 2009 in Room 920 East Building, 1:10-2:00 pm (Departmental Lecture Series)

Presented by Murad Ozaydin, Professor of Mathematics, University of Oklahoma

Abstract: There are theorems in discrete mathematics with con- tinuous proofs (sometimes with no other known proofs). Some examples are Lovasz’s proof of the Kneser Conjec- ture (on the chromatic number of certain graphs) and the prime power case of the Evasiveness Conjecture. These are consequences of classical theorems of topology such as the Borsuk-Ulam theorem or fixed point theorems of Lef- schetz and P. A. Smith. Another (which will be discussed in detail) is Alon and West’s solution (1986) of the Neck- lace Splitting problem: To split an open necklace with N types of gems (with an even number of identical gems of each type) fairly between two thieves N cuts suffice (no matter how many gems there are of each type, or how they are arranged on the necklace). Note that if we have the idiots necklace, i.e., all the rubies together, then all the emeralds, etc., we do need N cuts. The Borsuk-Ulam theorem, which is the key result, can and will be stated using only calculus. Only a little linear algebra may also be relevant in additional related material in convex geometry (if time permits).

Supertropical Algebras

Wednesday, September 9, 2009 in Room 920 East Building, 12:10-1:00 pm (Departmental Lecture Series)

Presented by Louis Rowen, Professor, Bar-Ilan University, Israel

Abstract: Tropical geometry is a new area of mathematics which enables one to study properties of algebraic surfaces by taking logarithms and letting their bases approach zero. In this talk, we present an algebraic structure which supports this theory and describe its properties.

Supertropical Matrix Theory

Tuesday, October 27, 2009 in Room 920 East Building, 12 noon (Departmental Lecture Series)

Presented by Louis Rowen, Professor, Bar-Ilan University, Israel

Abstract: In the previous talk, we discussed supertropical algebra as an algebraic framework for tropical geometry, focusing on roots of polynomials. In this talk (which is self-contained), we study matrices over supertropical algebras, and see how the theory parallels the standard theory of linear algebra (although there are a few surprises). Topics include versions of the determinant, the adjoint, the Hamilton-Cayley theorem, solutions of equations, and the rank of a matrix.

One sided quantum groups and the boson-fermion correspondence

Wednesday, April 9, 2008 in Room 920 East Building, 1:10 -2:00 PM (Departmental Lecture Series)

Presented by Earl Taft, Professor of Mathematics, Rutgers University

Abstract: We will review the quantum groups, which are noncommutative Hopf algebra deformations of the rational functions on the general and special linear groups. Then we will indicate some recent one-sided versions of these constructed by A. Lauve, S. Rodriguez and myself.  This in turn is related to a recent quantization of the boson-fermion correspondence of classical physics.

Order or Chaos? Understanding Careers in Different Labor Markets via Clusters for Nominal Longitudinal Data

Wednesday, April 30, 2008 in 920 HE, 1:10-2:00 pm (Departmental Lecture Series)

Presented by Marc A. Scott, Visiting Associate Professor at Hunter College and Associate Professor at Department of Humanities and Social Sciences, School of Education, New York University

Abstract: The speaker customizes techniques used in biological sequence analysis to generate homogeneous clusters for nominal longitudinal data in which the number of states is large. The outcomes are career trajectories through a space of “job types,” stratified by long-term economic mobility. He then uses information-theoretic measures to quantify the degree of order or chaos present in these trajectories over time. The clusters and information-theoretic techniques help refine our understanding of certain “stylized facts” about careers with different levels of mobility.

A Buckling Problem for Graphene Sheets

Wednesday, October 3, 2007 in 920 HE, 1:10-2:00 pm (Departmental Lecture Series)

Presented by Yevgeniy Milman, student in Hunter’s BA/MA Program in Mathematics

Abstract: The speaker develops a continuum model that describes the elastic bending of a graphene sheet interacting with a rigid substrate by van der Waals forces. Using this model, he studies a buckling problem for a graphene sheet perpendicular to a substrate. After identifying a trivial branch, he combines analysis and computation to determine the stability and bifurcations of solutions along this branch. Also presented are the results of atomistic simulations. The simulations agree qualitatively with the predictions of the continuum model but also suggest the importance, for some problems, of developing a continuum description of the van der Waals interaction that incorporates information on atomic positions. This research is based on Mr. Milman’s participation in the Research Experience for Undergraduates (REU) program at the University of Akron in Summer 2007.

Meta-Modeling with Kriging in the Design of a Product with Multiple Outcomes

Wednesday, October 10, 2007 in 920 HE, 1:10-2:00 pm (Departmental Lecture Series)

Presented by Terrence Murphy at School of Medicine,Yale University

Abstract: Engineers designing complex products routinely consider a number of outcomes whose desired performance characteristics place contradictory demands on the explanatory variables. In early design stages meta-models, i.e., statistically based models constructed from deterministic data, are used to emulate more sophisticated and computationally intensive simulations that are very accurate. We compare the performance of meta-models based on simple linear regression, Kriging, and splines to the very accurate design solutions yielded by finite element analysis (FEA) in the modeling of multivariate mechanical engineering data in the design of an auto-chassis. We find in our example that the Kriging models most closely reproduce the “true” solution yielded by the FEA simulations in a full information scenario and in some less than full information scenarios based on subsets of principal components.

3D Mathematica in the CUBE

Thursday, November 8, 2007 in 611 HN, 3:00 – 4:00 pm (Sigma Xi)

Presented by Mimi Tsuruga, student in Hunter’s BA/MA Program in Mathematics

Abstract: Mathematica is a math application and a powerful visualization tool capable of generating and rendering 2D and 3D objects with minimal lines of code. The CUBE (a six-walled CAVE) is a 3D virtual environment at the Beckman Institute at the University of Illinois at Urbana-Champaign. szgMathematica is a project which interfaces the Mathematica Kernel with the CUBE Front End. The CUBE has been used in psychology for experiments in spatial perception, in biology for studying models of viruses and in medicine for 3D virtual surgery. In this project a user can send a Graphics3D object using simple Mathematica code, move the object with a wand, walk into the object or fly through it on a user-defined curve. This program is ideal for people who want a “true 3D” visual understanding of complicated 3D surfaces.

Mathematica as a Powerful Authoring Tool for the Classroom

Wednesday, November 14, 2007 in 920 HE, 1:10-2:00 pm (Departmental Lecture Series)

Presented by John Kiehl, Adjunct Lecturer at Hunter College

Abstract: The newest release of the software package Mathematica trivializes the creation of animated and interactive charts, plots, and other graphics. The speaker will create stunning demonstrations within minutes that could be used in a lecture as self-discovery tools for students.

Propagation of Ultra-short Optical Pulses in Nonlinear and Random Media

Wednesday, November 28, 2007 in 920 HE, 2:10-3:00 pm (Departmental Lecture Series)

Presented by Tobias Schaefer at CUNY Graduate Center and College of Staten Island of CUNY

Abstract: The basic model for pulse propagation in optical media is the cubic nonlinear Schroedinger equation (NLSE). In the regime of ultra-short pulses, however, the basic assumption made in the derivation of the NLSE from Maxwell’s equations as a slowly varying amplitude approximation is not valid anymore. The speaker will give first a sketch of the derivation of the NLSE from Maxwell’s equations and then discuss applications of the basic model in the context of fiber optics. Then he will present a different approximation, the short-pulse equation and discuss its validity as well as its mathematical properties.

Ben Shahn’s Art and Mid-twentieth Century Science

Thursday, December 6, 2007 in 1203 HE, 1:00-2:00 pm (Co-sponsored by the Hunter College Chapter of Sigma Xi and the Thomas Hunter Honors Program)

Presented by Ezra Shahn, Professor of Biological Sciences at Hunter College

Abstract: Four years ago, Professor Shahn embarked on a study of the ways in which episodes in the history of science were reflected in contemporaneous works of art. Among recent artists, several studies had already noted that images of science played a significant role in a number of Ben Shahn’s works. As these were examined, it became clear that they were not random or artificial, but were actually based on advances in science that had been made only scant years before the art was created. In fact, these individual images had identifiable “sources” in the scientific literature, and, surprisingly, they also jointly represented an illustrated history of the development of the science of structural molecular biology that took place in the middle third of the last century.