Séminaires : Séminaire d'Algèbre

 In 2014, Leclerc gave a construction of a conjectural cluster structure on open Richardson varieties in types ADE. His construction was categorical in nature, involving preprojective algebra modules. His conjecture inspired work on cluster structures on braid varieties in arbitrary type, which generalize open Richardsons. Two cluster structures on braid varieties were recently constructed. The first one, based on ideas and techniques from symplectic topology, is due to Casals-Gorsky-Gorsky-Le-Shen-Simental. I will discuss the other, which is joint work with Galashin, Lam and Speyer. Our main geometric tool is the Deodhar decomposition. In type A, our quivers are given by "3D plabic graphs", which generalize Postnikov's plabic graphs for the Grassmannian. Time permitting, I will also discuss related work with Serhiyenko, where we show that for type A Richardsons, Leclerc's conjectural categorical construction does in fact give a cluster structure, with quivers again given by 3D plabic graphs.

This talk will be on Zoom only.