Purdue Mathematical Physics Seminar
In Spring 2026, the Purdue Mathematical Physics Seminar will be held on Tuesdays 10:30am - 11:30am Eastern time in MATH 215 (when we meet in person) unless otherwise noted.
SPRING 2026
March 3 (online)
Duncan Laurie (University of Edinburgh)
Zoom: to be provided
Title: Quantum toroidal algebras and their representations
Abstract: Quantum toroidal algebras Uq(g_tor) are the ‘double affine’ objects within the quantum setting. After reviewing and motivating the more well-studied finite and affine type quantum groups, we’ll introduce these algebras and outline a collection of new results. First, we shall construct double affine braid group and modular GL(2,Z) actions on Uq(g_tor). Then, using these, we will investigate the representation theory of quantum toroidal algebras, obtaining well-defined tensor products and (R-matrix) braidings for their principal module categories. Time permitting, I’ll mention work in progress with Théo Pinet which equips certain module subcategories with cluster algebra structures in type A, establishing generalised T-systems along the way.
March 24 (online)
Keyu Wang (University of Vienna)
April 3 (in-person)
Matthew Harper (Michigan State University)
Unusual time and location: SCHM 103, 11am-noon
April 14 (online)
Stefan Kolb (Newcastle University)
April 28 (in-person)
Pallav Goyal (UC Riverside)