Skip to main content

Cohomological Hall algebras and P=W conjecture

Posted in
Speaker: 
Alexandre Minets
Zugehörigkeit: 
University of Edinburgh/MPIM
Datum: 
Don, 14/12/2023 - 15:00 - 16:00
Location: 
MPIM Lecture Hall
Parent event: 
MPI-Oberseminar

Let S be a smooth surface, and Coh(S) the moduli stack of properly supported coherent sheaves on S. One can equip the Borel-Moore homology of Coh(S) with a convolution algebra structure; this is called the cohomological Hall algebra (CoHA) of S. While understanding CoHA algebraically is more or less hopeless for a general S, I will give an explicit presentation of its part, which corresponds to sheaves with zero-dimensional support. I will further explain how this presentation was used to prove the P=W conjecture of de Cataldo-Hausel-Migliorini about the perverse filtration on the cohomology of the Hitchin system of a smooth projective curve C.

© MPI f. Mathematik, Bonn Impressum & Datenschutz
-A A +A