Cohomological Hall Algebras of Zero-Dimensional Sheaves on Surfaces and the P=W Conjecture

Explore a comprehensive lecture on Cohomological Hall algebras (COHA) of zero-dimensional sheaves on surfaces and their connection to the P=W conjecture. Delve into the geometric constructions of infinite-dimensional quantum groups and their representations, focusing on the case of zero-dimensional sheaves on smooth surfaces. Examine the analogy between these structures and usual Hecke operators. Learn about the description of COHA in this context, based on joint work with Mellit, Minets, and Vasserot. Discover how this research contributes to a recent proof of the P=W conjecture by de Catlado, Hausel, and Migliorini, which relates the Hodge structure of character varieties to the perverse cohomology of the Hitchin fibration. Gain insights into this collaborative work involving Hausel, Mellit, and Minets, presented by Olivier Schiffmann from Université de Paris-Sud ORSAY at the M-Seminar, Kansas State University.