Coulomb branches and cluster varieties

Alexander Shapiro (University of Edinburgh)

Tuesday 10th February 16:00-17:00
Maths 311B

Abstract

Given a quiver \Gamma, Braverman, Finkelberg, and Nakajima define a non-commutative algebra A_\Gamma known in physics as the quantised K-theoretic Coulomb branch of the quiver gauge theory determined by \Gamma. In this talk, for \Gamma without 1-cycles I will construct quivers Q(\Gamma), such that the quantised algebra of global functions on the corresponding cluster variety is isomorphic to A_\Gamma. To that end I will use a presentation of A_\Gamma as a subalgebra inside a tensor product over the nodes of \Gamma of quantized phase spaces of multiplicative open Toda systems. This is a joint work with Gus Schrader, written in the most recent version of the preprint https://arxiv.org/abs/1910.03186.

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