Hunter College Mathematics Colloquium

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.