Cluster structures on braid varieties

Abstract: Many varieties in Lie theory--partial flag varieties, Schubert varieties, moduli of local systems on surfaces--admit cluster structures, which give a combinatorial way of encoding quantum deformations of these varieties. Braid varieties give a unifying framework for constructing these cluster structures. I will start by defining braid varieties and give some motivations coming from knot homology and mirror symmetry. Then I will introduce the main tool, Legendrian weaves, which allow us to construct clusters in a concrete and diagrammatic way. The diagrams will be familiar to anyone who has seen Soergel calculus. This is joint work with Roger Casals, Eugene Gorsky, Mikhail Gorsky, Linhui Shen and Jose Simental.

algebraic geometryrepresentation theory

Audience: researchers in the topic

Algebra and Geometry Seminar @ HKUST

Series comments: Algebra and Geometry seminar at the Hong Kong University of Science and Technology (HKUST).

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