Combinatorics and Algebra Seminar-Noncommutative algebra from a geometric point of view

Date and time: Friday, February 4, 3-4pm

Place: Phillips 736

Speaker: Xingting Wang, Howard

Title: Noncommutative algebra from a geometric point of view

Abstract: In this talk, I will discuss how to use algebro-geometric and Poisson geometric methods to study the representation theory of 3-dimensional Sklyanin algebras, which are noncommutative analogues of polynomial algebras of three variables. The fundamental tools we are employing in this work include the noncommutative projective algebraic geometry developed by Artin-Schelter-Tate-Van den Bergh in 1990s and the theory of Poisson order axiomatized by Brown and Gordon in 2002, which is based on De Concini-Kac-Priocesi’s earlier work on the applications of Poisson geometry in the representation theory of quantum groups at roots of unity. This is joint work with Milen Yakimov and Chelsea Walton.