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 […]
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 […]
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 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 […]
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 […]
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 […]
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.
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 […]
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 […]
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 […]
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 […]
