Cohomological Hall Algebras of 2-Calabi-Yau Categories and Applications - Lecture 2

Explore the second lecture in a four-part series on Cohomological Hall algebras (CoHAs) of 2-Calabi-Yau categories and their applications, delivered by Lucien Hennecart from the University of Edinburgh. Delve into the interactions between CoHAs and key questions in algebraic geometry and representation theory, including enumerative geometry and Kac-Moody algebras. Examine the CoHA structures on Borel-Moore homology of object stacks in various Abelian categories, such as sheaves on surfaces, quiver representations, and fundamental group representations. Discover how CoHAs provide insights into the cohomology of stacks and moduli spaces, addressing conjectures on cohomological integrality, positivity, and purity. Learn about the geometric construction of generalised Kac-Moody algebras using CoHAs, and gain an understanding of their applications to quiver varieties and nonabelian Hodge theory. This 80-minute lecture, part of the M-Seminar at Kansas State University, offers an in-depth exploration of CoHAs and their significance in modern algebraic geometry and representation theory.