题目: Legendrian weaves and cluster algebra

报告人：翁达平，UC Davis

时间: 2023年7月5日、7月6日、7月12日、 7月13日, 上午9：30开始

地点：东区第二教学楼2402教室

摘要: Legendrian weaves were introduced by Casals and Zaslow in 2020 as a combinatorial description of certain Legendrian surfaces in the standard contact R^5. In many cases, the Lagrangian projection of these Legendrian surfaces gives exact Lagrangian fillings of Legendrian links. The Kashiwara-Schapira moduli space of such a Legendrian link carries a cluster structure, and the combinatorics of this cluster structure is again nicely captured by Legendrian weaves. Legendrian weaves provide a new symplectic perspective on many known cluster structures, including positroid strata in Grassmannian and double Bott-Samelson cells, and give us a new geometric understanding of Donaldson-Thomas transformations on cluster varieties. In this lecture series, we will discuss some basics of Legendrian weaves and cluster structures, and give many examples demonstrating the close connection between them. If time allows, we will also discuss the new construction of cluster structures on braid varieties by Casals, Gorsky, Gorsky, Le, Shen, and Simental.