Integer partitions are ubiquitous in mathematics, arising in subjects as disparate as algebraic combinatorics, algebraic geometry, number theory, representation theory, to mathematics physics. Many of the deepest results on partitions […]
The classical oddtown and eventown problems involve a collection of subsets of a finite set with an odd (resp. even) number of elements such that all pairwise intersections contain an even number of elements. In this talk, we will discuss these results as well as the following variants: We consider set sizes and pairwise intersection […]
Quandles are algebraic structures encoding the motion of knots through space. Quandle cocycle quivers categorify the quandle cocycle invariant. In this talk we will define a quiver representation associated to […]
Let K be a compact convex set in the Euclidean space R^n. How many lights are needed to illuminate its boundary? A classical conjecture of Boltyanskii (1960) asserts that 2^n […]
Following Kalashnikov, we recover Givental’s small J function for CP^1 by viewing it as a quiver flag variety.
Following Kalashnikov, we recover Givental’s small J function for CP^1 by viewing it as a quiver flag variety.
We’ll first define the two-point gravitational correlators which appeared last week as descendant Gromov-Witten invariants. By request, we’ll then introduce Gromov-Witten invariants as they appear in the expository work https://arxiv.org/abs/2501.03232 and give CP^1 to demonstrate some of the identities which GW invariants satisfy. If time allows, we’ll also give the small and big quantum cohomology for CP^1.
I will present an integral — requiring no character twists — converse theorem for recognizing when is a Dirichlet series with algebraic integer coefficients equal to the L-function of a modular form. This […]
A big area in combinatorics over the last several decades has been the study of pattern-avoiding permutations, whose enumeration is exciting and mysterious. Alternating sign matrices (ASMs) are a generalization […]
Large Language Models like ChatGPT rely on surprisingly familiar mathematics. This talk will explore how ideas from (linear) algebra, number theory and combinatorics appear — both directly and indirectly — […]
A Jacobian variety is a principally polarized abelian variety (PPAV) associated with a smooth complex algebraic curve. For dimensions less than or equal to 3, every PPAV is either a […]
The recognition that theoretical models of natural language syntax have robust algebraic foundations is longstanding. Both the syntactic structures proposed (trees, semirings, etc.) and metrics developed to understand them (the […]
