Upcoming and Past Seminars
History: The HCMC (formely known as the Hunter College Applied Mathematics (HCAM) Seminar) was initiated by the late John Arthur Loustau, a former professor of the Mathematics and Statistics Department here at Hunter, with his then post-doc Emmanuel Asante-Asamani in 2018. John had an eclectic mix of mathematical interests, each of which he pursued with gusto and depth. In a career spanning nearly 50 years, he began his journey in Commutative Algebra, transitioned afterwards to Computer Science, then Numerical Analysis, and eventually into Mathematical Biology. John recounted once a vacation he took with his family to Reno long ago. His father, a hardware merchant who also did plumbing and electric work, had taken him to the School of Mining Engineering at University of Nevada and told John that he had once dreamt of enrolling there when he was younger. Nevertheless, as John fondly recalled, he was a fine applied mathematician.
In the spirit of John's open-mindedness and willingness to foster and maintain a diverse community in mathematics, HCMC hosts speakers across a wide range of disciplines, from both academia and industry. HCMC also showcases the work of rising graduates from various tracks in our Mathematics MA program at Hunter and regularly hosts BA, BA/MA, and MA alumni to share their post-graduate experiences with current students. If you are interested in giving a talk at this seminar, please contact vrmartinez@hunter.cuny.edu
Spring 2024 (Current)
February 2: Rob Thompson (CUNY Hunter College)
February 29: Kisung You (CUNY Baruch College)
March 28: Robert Ghrist (University of Pennsylvania)
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.