Geometry/Physics Seminar

Title: Cluster structures on braid varieties
Speaker: Linhui Shen
Speaker Info: Michigan State University
Brief Description:
Special Note:

Let G be a complex semisimple group. Let \beta be a positive braid whose Demazure product is the longest Weyl group element. The braid variety M(\beta) generalizes many well known varieties, including positroid cells, open Richardson varieties, and double Bott-Samelson cells. We provide a concrete construction of the cluster structures on M(\beta), using the weaves of Casals and Zaslow. We show that the coordinate ring of M(\beta) is a cluster algebra, which confirms a conjecture of Leclerc as special cases. As an application, we show that M(\beta) admits a natural Poisson structure and can be further quantized. This talk is based on joint work with Roger Casals, Eugene Gorsky, Mikhail Gorsky, Ian Le, and Jose Simental.
Date: Wednesday, May 10, 2023
Time: 3:00pm
Where: Lunt 107
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