Mirror symmetry and canonical bases for quantum cluster algebras

Travis Mandel
Univ. of Edinburgh
Tuesday, December 3, 2019 - 3:30pm to 4:30pm
Vincent Hall 16

Mirror symmetry is a phenomenon which relates the symplectic geometry of one space X to the algebraic geometry of another space Y. One consequence is that a canonical basis of regular functions on Y can be defined in terms of certain counts of holomorphic curves in X. I'll discuss the application of this to (quantum) cluster algebras --- certain combinatorially defined algebras whose definition was motivated by the appearance of canonical bases in representation theory and Teichmüller theory.