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
Spring 2026
Date: Monday, February 2, 2026
Speaker: Gautam Chinta
Title: Sums of integers and their powers
Abstract: Everybody knows that 1+2+...+n=n(n+1)/2. You probably even know the formulas for the sum of the first n squares and cubes. On YouTube you can find videos asserting that the (infinite) sum of all the positive integers is -1/12. What does this mean and how is it related to the results above? We will provide a context for these results and explain ideas of Euler, Riemann and Zagier.
Date: Monday, February 9, 2026
Speaker: CANCELLED
Title: TBA
Abstract: TBA
Date: Monday, February 16, 2026
Speaker: COLLEGE CLOSED
Title: TBA
Abstract: TBA
Date: Monday, February 23, 2026
Speaker: CANCELLED
Title: TBA
Abstract: TBA
Date: Monday, March 2, 2026
Speaker: Anna Pun
Title: The Stable Tamari Lattice
Abstract: The Tamari lattice is a partial order that appears in several equivalent Catalan models, including parenthesizations, binary trees, Dyck paths, and triangulations of convex polygons. Originally defined in terms of different ways of parenthesizing a product, it has become a central object in combinatorics.
In this talk, I will describe an extension of this structure, called the stable Tamari lattice. After reviewing the original construction and its combinatorial intuition, I will explain how the stable version supports comparisons across families of objects and gives rise to new structural phenomena.
I will present concrete examples and recent results concerning intervals, covering relations, and structural statistics in this lattice, and discuss some of the questions that currently guide our work.
Date: Monday, March 9, 2026
Speaker: Stephen Preston
Title: Generalized Rossby-Haurwitz waves in 2D and 3D
Abstract: Rossby-Haurwitz waves are explicit exact nonsteady solutions of the 2D Euler equation on the sphere, arising from a perturbation around steady rotation. We show how to obtain other solutions to the Euler equations on a variety of other manifolds, particularly in three dimensions, including explicit formulas on the three-sphere. The main idea is to work with velocity fields which generate isometries and whose vorticity fields also generate isometries, and we give a classification theorem for these as well. This is joint work with Patrick Heslin
Date: Monday, March 16, 2026
Speaker: Ioakeim Ampatzoglou
Title: An introduction to statistical mechanics
Abstract: In this talk, we will introduce foundational topics in statistical mechanics. Namely, we will show the emergence of the Boltzmann equation from finitely many interacting particle systems in the Boltzmann-Grad scaling limit. Then, we will discuss the main properties of the equation such as weak formulation, conservation laws, and the famous H-theorem. The talk will be self-contained and will not assume any prior knowledge of statistical mechanics.
Date: Monday, March 23, 2026
Speaker: Heidi Goodson
Title: An Introduction to Sato-Tate Distributions
Abstract: In this talk I will give an overview of the area of research that has been on my mind for the last decade. This topic starts with a simple question: How many points are there on a given curve over a finite field F_p? In this talk I will explain what this question means and show you concrete examples that may convince you that the answers to this and related questions are interesting. I will describe some tools and techniques that are available when working on these problems and what happens when things fall apart and the techniques are insufficient. Examples, questions, and confusions will be presented throughout the talk. This area of research lies in the field of arithmetic geometry, but I plan to present in a way that doesn't require any background in this.
Date: Monday, March 30, 2026 (Starts 4:45 PM)
Speaker: Weilin Li
Title: Fourier matrices and super-resolution
Abstract: Fourier matrices are special structured matrices that are parameterized by a node set. The first half of this talk explains the problem of quantifying the smallest singular value of a Fourier matrix in terms of the "geometry" of the nodes. The second half of this talk centers on the super-resolution problem of recovering fine details from noisy coarse observations. In particular, we show that a certain algorithm has super-resolution capabilities and discuss consequences of this analysis.
Date: Monday, April 13, 2026
Speaker: NO PIZZA SEMINAR (Special Departmental Colloquium Event)
Title: N/A
Abstract: N/A
Date: Monday, April 20, 2026
Speaker: Delaram Kahrobaei
Title: Post-quantum Group-based Cryptography in the AI Era
Abstract: In this talk, I will highlight how group theory can inform both the design and analysis of post-quantum primitives, and how AI is reshaping the practical security picture. I will first discuss lessons from the Semidirect Discrete Logarithm Problem (SDLP); including why SDLP-based constructions over finite groups turn out to be quantum-easy; then pivot to directions that appear more promising, such as post-quantum hash functions built from expander/Cayley-graph phenomena in higher-dimensional SLn(Fp) and the Spinel hash-based signature framework. I will also emphasize a complementary hardness pillar: recent results showing that discrete logarithm in certain classes of finitely generated infinite groups can yield NP-hard instances, opening new avenues for post-quantum assumptions beyond the usual lattice/code/isogeny families. Finally, I will connect this to the “AI era”: machine-learning methods that learn effective heuristics for algebraic decision problems (e.g., conjugacy) and for NP-complete foundations (e.g., graph k-colorability), underscoring why instance hardness and AI aware evaluation must be part of any credible PQC story.
Date: Monday, April 27, 2026
Speaker: Brian Allen
Title: Scalar Curvature and Convergence of Riemannian Manifolds
Abstract: To what extent does curvature control topology? We begin by introducing the geometric ideas necessary to appreciate the Gauss–Bonnet theorem, and use it as a guiding example of how an integral curvature condition determines a topological invariant. Motivated by this model, we then discuss scalar curvature from a geometric viewpoint, interpreting it via volume comparison of small metric balls. We explore several rigidity theorems in which lower scalar curvature bounds impose strong topological restrictions, and conclude by examining recent developments on the stability of these results under geometric convergence.
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.