Algebra / Number Theory / Combinatorics Seminar

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 […]

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 […]

Biquandle arrow weights invariants are enhancements of the biquandle counting invariant for oriented virtual and classical knots defined from biquandle-colored Gauss diagrams using a tensor over an abelian group satisfying […]

An inner amenable group is one in which there is a finitely additive conjugation-invariant probability measure on the non-identity elements.  In this talk, we show that inner amenability is not […]

A graphical design is a quadrature rule for a graph inspired by classical numerical integration on the sphere. Broadly speaking, that means a graphical design is a relatively small subset […]

A Z-module M in a number field K gives rise to a lattice in the corresponding Euclidean space via Minkowski embedding. Such lattices often carry inherited structure from the number […]