Cohomological Hall Algebras of 2-Calabi-Yau Categories and Applications - Lecture 4

Explore the fourth lecture in a 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, focusing on enumerative geometry and Kac-Moody algebras. Examine the CoHA structures in various categories, including sheaves on surfaces, quiver representations, and fundamental group representations. Discover how CoHAs provide insights into the cohomology of stacks and moduli spaces, and their role in addressing conjectures on cohomological integrality, positivity, and purity. Learn about the geometric construction of generalized Kac-Moody algebras using CoHAs, and investigate applications to quiver varieties cohomology and nonabelian Hodge theory. Gain valuable knowledge from this independent lecture, which draws from collaborative work with Ben Davison and Sebastian Schlegel Mejia.