Cohomological Hall Algebras of 0-Dimensional Sheaves on Surfaces

Explore the intricacies of cohomological Hall algebras (COHAs) of 0-dimensional sheaves on surfaces in this advanced mathematics lecture. Delve into the construction of COHAs from abelian categories of low homological dimension, with a focus on coherent sheaves on smooth surfaces. Examine the explicit description of the COHA for 0-dimensional sheaves, building upon the foundational work of Nakajima and Lehn. Discover how this description can be applied to derive structural results about cohomology of moduli spaces of sheaves with positive-dimensional support. Learn about the recent proof of the P=W conjecture and gain insights into joint research conducted with A. Mellit, O. Schiffmann, and E. Vasserot. This in-depth talk, presented by Alexandre Minets from MPI, Bonn, offers a comprehensive exploration of cutting-edge developments in algebraic geometry and representation theory.