Events

We will give an introduction to nets of associative algebras over discrete metric spaces, which arise in mathematical physics as axiomatizations of the observables content of quantum field theories over discrete spaces. We will present examples arising naturally from combinatorics and representation theory, and discuss some recent structural results about these objects. Speaker's website: https://www.coreyjonesmath.com/

The theory of integral closure of ideals, originating in the early twentieth century with work of Krull, Zariski, Rees, and others, remains a vibrant area of research in algebraic geometry, commutative algebra, and singularity theory. This theory's significance partly stems from its connections with numerical invariants such as multiplicities. During the 1950s, significant advances by…

A representation of the category of finite sets is a linear algebraic object, which roughly consists of a sequence of representations V_n of the symmetric group S_n related by transition maps.  These representations occur naturally in several places including in the study of Kazhdan-Lusztig polynomials of braid matroids, the homology of moduli spaces of curves,…

Motivated by the problem of classifying quantum symmetries of non-semisimple, finite-dimensional associative algebras, we define a notion of connection between bounded quivers and build a bicategory of bounded quivers and quiver connections. We prove this bicategory is equivalent to a bicategory of basic algebras,  bimodules, and intertwiners with some additional structure. Speaker’s website: https://math.sciences.ncsu.edu/people/sthomps6/

Finding combinatorial interpretations for the structure constants of Schubert polynomials is a long-standing open problem in algebraic combinatorics. In the case where one of the Schubert polynomials is a Schur polynomial, the structure constants are encoded in a poset called the “k-Bruhat order”. In studying the k-Bruhat order, Bergeron and Sottile were led to introduce…

Noncrossing partitions and nonnesting partitions are both counted by Catalan numbers. Noncrossing partitions on admit a natural cyclic action of order 2n, induced by the Kreweras complement. Nonnesting partitions admit a natural toggle-based action; in fact, they admit one such action for each choice of Coxeter element of the symmetric group. We prove that the latter actions all…