Graduate Student Colloquium
Graduate Student Colloquium
2025-2026
2025-2026
The Graduate Student Colloquium is geared towards introducing graduate students to different areas of mathematics. Each week a different member of the Graduate Center Mathematics Department faculty will discuss a topic that is accessible to all graduate students. All graduate students without an advisor are required to attend, but even those with an advisor are welcome!
All meetings of the Graduate Student Colloquium will be held on Mondays from 4:00-6:00 PM in person at the Graduate Center Room 6417, unless otherwise stated.
Organizers:
George Monge: gmonge@gradcenter.cuny.edu
Oren Bassik: obassik@gradcenter.cuny.edu
Reilly Fortune: rfortune@gradcenter.cuny.edu
Adrian Cabreja: acabreja@gradcenter.cuny.edu
Professor John Terilla: JTerilla@gc.cuny.edu
Fall 2025
Date: Monday, September 8, 2025
Speaker: John Terilla
Title: A cell decomposition on the set of fixed points of an adjunction.
Abstract: The set of fixed points of an adjunction related to Isbell duality (which is like the set of eigenvectors of M M^t for a linear operator M) has some interesting geometric/combinatorial structure. I’ll walk through an example and illustrate a cell decomposition of the set of fixed points which is cut out by tropical hyperplanes.
Date: Monday, September 15, 2025
Speaker: Daniel Ginsberg
Title: Shock waves in compressible fluids.
Abstract: The compressible Euler equations describe the time-evolution of gases. They form a quasilinear system of hyperbolic PDE and as such, develop singularities in finite time. One physically-important type of singularity is a "shock wave" (think the sonic boom of a jet breaking the sound barrier). In this talk, I will give a brief introduction to the study of these singularities and will discuss recent work on their long-time behavior.
Date: Monday, October 6, 2025
Speaker: Indranil SenGupta
Title: From Chance to Choice: Exploring Stochastic Finance
Abstract: Ever wondered how mathematicians model the ups and downs of financial markets? Probability theory and stochastic processes provide the tools to do just that, capturing the random evolution of stock prices, interest rates, mortgage rates, and other risk factors. These ideas form the backbone of modern quantitative finance. A classic example is Brownian motion, which underlies the Nobel Prize–winning Black–Scholes-Merton model. More broadly, jump processes and stochastic volatility models capture sudden market shocks and complex dynamics. In this talk, I will offer an accessible introduction to stochastic processes in finance and highlight recent advances and open research questions for graduate students—no prior background in finance required!
Date: Monday, October 27, 2025
Speaker: Mikael Vejdemo-Johansson
Title: Modules and representations are key to topological data analysis
Abstract: Topological Data Analysis draws on algebraic topology to construct methods of data analysis that by the properties of topological methods turn out to be noise-resistant, deformation-invariant, and often very highly compressed. The core method is persistent homology, which allows a global, scale-invariant perspective on scale-dependent constructions. Introduced in a computational geometry context, persistent homology started out in the year 2000 as an algorithm for finding a pairing of simplices in a total order of simplices in a simplicial complex.
Since then, the research field has developed explosively. Notably, there has been a number of large steps progressing both our understanding of what topological methods can do with data, and how to build more efficient algorithms - many of which are founded in a more refined choice of algebraic abstractions for representing the underlying concepts. Modules over a polynomial ring, representations of quivers, representations of partial or total orders, as well as sheaves of modules over a cellular complex all are algebraic abstractions that when introduced had a deep impact on the field.
In this talk, I will introduce the basics of topological data analysis, and describe some of these algebraic abstractions and the impact they have had on research in the field. In addition to being a viable area to find applications of algebraic topology, TDA and persistence also provide an example for how large a difference an apt choice of abstractions can make.
Date: Monday, November 3, 2025
Speaker: CANCELLED
Title: TBA
Abstract: TBA
Date: Monday, November 10, 2025
Speaker: Karol Koziol
Title: Galois groups, Galois Representations, and the Langlands Program
Abstract: Topics on various aspects of the (local) Langlands Program, specifically representation theory of p-adic reductive groups and Galois representations.
Date: Monday, November 17, 2025
Speaker: CANCELLED
Title: TBA
Abstract: TBA
Date: Monday, November 24, 2025
Speaker: Alexey Ovchinnikov
Title: Solving polynomial systems
Abstract: We will discuss and compare several approaches to solving polynomial systems of equations.
Date: Monday, December 1, 2025
Speaker: Guy Moshkovitz
Title: Bilinear equations
Abstract: We will show how to analyze any system of bilinear equations (not linear equations, which we already understand!). Namely, we will show how its number of solutions depends on its algebraic structure. We will also see how graph theory plays an important role in this question.
Date: Monday, December 8, 2025
Speaker: Emilio Minichiello
Title: Introduction to Graph Homotopy Theory
Abstract: In this talk I'll survey the field of graph homotopy theory, a relatively new and vibrant subject that applies the abstract mathematics of algebraic topology to graph theory. I'll introduce the two most prominent areas of this subject: x-homotopy theory and A-homotopy theory. I'll try to motivate these different areas with results from combinatorics like Lovasz' proof of the Kneser conjecture and Maurer's work on matroid basis graphs, and I'll survey what is known in these areas. If there is time I'll talk a bit about my own work on model categories for x-homotopy theory.