Tudor Pădurariu (CNRS-Université Pierre et Marie Curie-Université Paris Diderot)
Title: Coherent sheaves on the commuting stack
Abstract: I will talk about the derived category of the commuting stack of two matrices, alternatively of the moduli stack of dimension zero sheaves on the affine space of dimension two. In previous work, we constructed semiorthogonal decompositions of this category in smaller categories, called quasi-BPS categories, which we believed to be indecomposable, and we computed their (localized equivariant or
topological) K-theory. In the current work, we compute the quasi-BPS categories. As a corollary, we prove a conjecture of Negut about relations between Hecke correspondences, and a conjecture of Gorsky-Negut about the generation of the derived category of the commuting stack. Based on previous joint work with Yukinobu Toda, we obtain a dimension three version of the Bridgeland-King-Reid and Haiman derived equivalence. This is joint work with Sabin Cautis and Yukinobu Toda (in progress).
Location: in person at UQAM PK-5675
or online at Zoom meeting 86352363947