- Daping Weng, MSU
- Double Bott-Samelson cell and the moduli space of microlocal rank-1 sheaves
- 10/01/2019
- 3:00 PM - 4:00 PM
- C204A Wells Hall
Shende, Treumann, and Zaslow gave a combinatorial description of the moduli space of microlocal rank-1 sheaves in their paper “Legendrian Knots and Constructible sheaves”. Following a result of Guillermou, Kashiwara, and Schapira, this moduli space is an invariant of Legendrian links. In this talk, I will review the definition and the cluster structure on the (undecorated) double Bott-Samelson cells, and show that in the cases of positive braids of Dynkin type A_r, the undecorated double Bott-Samelson cells are isomorphic to moduli spaces of microlocal rank-1 sheaves associated to the corresponding braid closures. As a corollary, the undecorated double Bott-Samelson cells of Dynkin type A_r are also Legendrian link invariants for positive braid closures. If time allows, I will also talk about how to count F_q points on the undecorated double Bott-Samelson cells.