Algebra / Number Theory / Combinatorics Seminar

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 […]

Given any finite set of integer points S, there is an associated function f_S that encodes S, which we call its integer point transform.   One can think of this integer […]

The Riemann–Hilbert correspondence relates algebra to differential equations on complex algebraic varieties. In characteristic p, there is an analogous correspondence due to Emerton–Kisin and later generalized by Bhatt–Lurie, where the […]

It is a fundamental question to find rational solutions to a given system of polynomials, and in modern language this translates into finding rational points in algebraic varieties.  It is […]

Let $C$ be a nice (smooth, projective, geometrically integral) curve over a number field $k$. The single most important geometric invariant of a curve is the genus, which can control […]

This talk explores elementary probability and statistics through the language of category theory. We introduce a category of Bundles and use it to reinterpret several results typically covered in an […]

I will talk about some results concerning the non-vanishing of $L$-functions associated to fixed order characters $\ell$ at the central point over functions fields. Quadratic characters have been studied a […]

Hunter's theorem ensures that the complete homogeneous symmetric (CHS) polynomials of even degree are positive definite functions.  We provide new proofs of Hunter's theorem, applications to operator theory, and a […]

Virtual links can be represented as equivalence classes of Gauss diagrams under Reidemeister moves. The Forbidden Moves are moves which look plausible but change the virtual isotopy class of the […]

We will examine the multiplicative structure of two skein algebras--- the usual Kauffman bracket skein algebra of a surface (generated by loops) and a generalization of it due to Roger-Yang […]

This is a talk in two parts covering two projects that the speaker mentored over the summer of 2025. The first project deals with the study of polytopes that arise […]

The classical Siegel's lemma (1929) asserts the existence of a nontrivial integer solution to an underdetermined integer homogeneous linear system, whose "size" is small as compared to the size of […]