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. For Zoom meetings, use the link
https://purdue-edu.zoom.us/j/98588621708?pwd=9a21yDxedyTWrzbFhZPqbigKosV9Qc.1 (passcode: 808095)
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 13 (in-person)
Daniil Klyuev (Northwestern University)
Unusual time and location: MATH 631, 11am-noon
Title: q-characters in Yangian category O via the sphere trace
Abstract: I will talk about twisted traces on quantized quiver Coulomb branches (truncated shifted Yangians.) Any Verma module over a quantized Coulomb branch gives rise to a twisted trace. This trace contains the information about the q-character of the shifted Yangian acting on this module. For conical Coulomb branches there is also a trace introduced by Gaiotto and Okazaki ("sphere trace"). I will show how the sphere trace allows us to compute the q-character of certain simple objects in Yangian category O. Based on joint work in progress with Vasily Krylov.
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)