# Memento

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# Cluster structures on braid varieties

#### Event details

 Date 19.05.2022 – 13:15 › 15:00 Speaker José Simental Rodriguez (Max Planck Institute for Mathematics, Bonn) Location Category Conferences - Seminars Event Language English

Given a simply-laced complex simple Lie group and an element $\beta$ of its positive braid monoid, we construct an algebraic variety $X(\beta)$ called the braid variety. These are smooth, affine varieties that generalize many well-known varieties in Lie theory, including open Richardson varieties. In joint work with Roger Casals, Eugene Gorsky, Mikhail Gorsky, Ian Le and Linhui Shen, we give an explicit cluster structure to the coordinate ring of $X(\beta)$ using the combinatorics of algebraic weaves. In particular, this shows that open Richardson varieties are cluster varieties.

## Practical information

• Informed public
• Free

## Organizer

• Oscar Kivinen