Affine BPS Algebras and W Algebras - Lecture on Quiver Potentials and Cohomological Hall Algebras

Explore a comprehensive lecture on Affine BPS algebras and W algebras delivered by Ben Davison from the University of Edinburgh at the M-Seminar, Kansas State University. Delve into the intricacies of BPS Lie algebras associated with quivers and potentials, examining their role in generating Kontsevich-Soibelman cohomological Hall algebras (CoHA) and categorizing BPS invariants. Discover how special cases of CoHAs relate to Schiffmann and Vasserot's work on the AGT conjecture. Learn about the affinization of BPS Lie algebras and their expression as universal enveloping algebras. Investigate the three-loop quiver with its canonical cubic potential, uncovering its connection to differential operators on the complex torus. Gain insights into the spherical generation of associated CoHAs and their description in terms of the affine Yangian of gl(1). This 1-hour 19-minute talk offers a deep dive into advanced algebraic concepts and their applications in theoretical physics and mathematics.