Bridges between lattice models, representation theory and number theory

Speaker(s) Henrik Gustafsson Umeå University
Date 23 August 2022 – 10:00 to 11:00
Venue INI Seminar Room 1
Session Title Bridges between lattice models, representation theory and number theory
Event [NC2W02] Crossing the bridge: New connections in number theory and physics
Abstract

I will give an overview of a series of papers joint with Ben Brubaker, Valentin Buciumas and Daniel Bump on Whittaker functions for reductive groups over non-archimedean fields and their metaplectic covers. 

In particular, I will focus on how these special functions in representation theory can be described by certain two-dimensional lattice models, and give a detailed explanation in a simple case. This allows for the use of a wide array of tools from statistical mechanics. 

Whittaker functions are also important in number theory which I will briefly discuss, thus forming a bridge between the two central themes of the workshop: number theory and physics.

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