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Bridges between lattice models, representation theory and number theory

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NC2W02 - Crossing the bridge: New connections in number theory and physics

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.

This talk is part of the Isaac Newton Institute Seminar Series series.

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