Algebra and Combinatorics Seminar

Date: April 27, 2018

Time: 3:00PM - 4:00PM

Location: BLOC 628

Speaker: Xingting Wang, Temple University

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 talk demonstrates a strong connection between noncommutative algebra and geometry when the underlining algebra satisfies a polynomial identity or roughly speaking is almost commutative.