Binghamton Math GSS

Fall 2026 Schedule

• Aug. 21st
  Speaker:
  Title: Welcome Party!
  
  Abstract: Open to all graduate students! We will have food and drinks, feel free to bring board games or anything else you see fit.

• Aug. 28th
  Speaker: Sylvia Medlin
  Title: Ideal Triangulations of Knot Complements

Abstract:
Given a knot $K\subset \mathbb S^3$, the complement $\mathbb S^3 \setminus K$ often admits an interesting geometric structure that allows one to distinguish it from other knots. An ideal triangulation of $\mathbb S^3 \setminus K$ is a combinatorial structure that one can use to determine whether the knot complement admits a hyperbolic structure and, if they exist, to parametrize them. In this talk, I will introduce methods for producing ideal triangulations of a knot complement and how to use them to compute hyperbolic structures.

• Sep. 4th
  Speaker: Eric Yin
  Title: Representation Theory over Fields of Any Characteristic

Abstract:
The representation theory of finite groups over the complex numbers, or more generally a field of characteristic zero, is largely concerned with understanding irreducible representations, as due to Maschke's theorem, all other representations can be written as direct sums of irreducible representations. Moving to fields with arbitrary characteristic, Maschke's theorem no longer holds in general, and thus understanding irreducible representations is no longer sufficient. In this talk we discuss a module-theoretic perspective of representation theory, and how classical theorems of representation theory over C can be generalized to results about representation theory over any algebraically closed field.

• Sep. 11th - Rosh Hashanah

• Sep. 18th
  Speaker: Levi Axelrod
  Title: Using Gerrymandering to Prove Nonembeddability Theorems

Abstract:
We consider a method for creating simplicial complexes that don't embed into real euclidean spaces, for instance the complete graph $K_5$ into $\R^2$ or $\RP^2$ into $\R^3$. Nonembeddability will follow from the Borsuk-Ulam Theorem, and will use tools such as deleted joins, Alexander duality, and Bier spheres, which will be introduced in the talk. These tools come together nicely when a certain combinatorial condition holds, which coincides with methods for gerrymandering an election between two parties.

• Sep. 25th
  Speaker: Yahong Yang
  Title: Mathematical Intuition for Machine Learning

Abstract:
In this talk, I will share some mathematical insights into neural networks, with a particular focus on solving partial differential equations. I will discuss some of the main difficulties that arise when using neural networks for PDE problems and how mathematical ideas can help us understand and overcome these challenges.

More broadly, I would like to present a few perspectives on both Math for AI and AI for Math, and also briefly introduce some topics that I hope to include in future courses.

• Oct. 2nd
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• Oct. 9th
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• Oct. 16th
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• Oct. 23rd
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• Oct. 30th
  Speaker: Robert Rust
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• Nov. 6th
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• Nov. 13th
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• Nov. 20th
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• Nov. 27th - Thanksgiving Break

• Dec. 4th
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• Previous Semesters