Mathematical Physics and Harmonic Analysis Seminar

Date: October 26, 2018

Time: 1:50PM - 2:50PM

Location: BLOC 628

Speaker: Dylan Allegretti, University of Sheffield

Title: Categorified canonical bases and framed BPS states

Abstract: In a famous paper from 2006, Fock and Goncharov introduced a moduli space of framed PGL(2,C)-local systems on a surface with boundary. This moduli space has the structure of a cluster variety, and the algebra of regular functions on this cluster variety has a canonical vector space basis. In this talk, I will describe a family of graded vector spaces which categorify Fock and Goncharov's canonical basis. In certain cases, these vector spaces arise as the cohomology of moduli spaces of stable quiver representations as predicted by the physics of BPS states in N=2 field theories.