**Thursdays, 4:30-5:30pm, (room to be determined for Spring 2023),
(currently hosted in hybrid format: Zoom Link for Remote Access).
**

He was a fine applied mathematician.

In the spirit of John's open-mindedness and willingness to foster and maintain a diverse community of 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 me at vrmartinez-at-hunter-dot-cuny-dot-edu.

**Spring 2023 Schedule**

**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.

*
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.

*
Hiatus
*

*
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.

*
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
*

**Current Seminar**

**Past Seminars**