Braid varieties and cluster structures

Date: Thursday 28 July 2022

Abstract

I will introduce braid varieties and explain how they generalize Richardson varieties. I will motivate cluster structures on Richardson varieties through two perspectives:

1) Braid varieties turn out to be log Calabi-Yau, so that one can formulate mirror symmetry between braid varieties. This leads to statements like the Fock-Goncharov duality conjectures.

2) On the other hand, braid varieties are a kind of generalization of moduli spaces of local systems, so that they can be studied in the context of Hitchin systems.

This leads one to study weave calculus, which is a degenerate version of Soergel calculus.