Okounkov's Conjecture via BPS Lie Algebras

Explore an advanced mathematics seminar where Dr. Ben Davison from the University of Edinburgh presents a proof of Okounkov's conjecture through the lens of BPS Lie algebras. Delve into the theory of stable envelopes and R matrices used by Maulik and Okounkov to define a new type of Yangian algebra, which exists as a subalgebra of the endomorphism algebra of equivariant cohomology in Nakajima quiver varieties. Learn how this algebra relates to ADE Dynkin diagrams and one-loop quivers, and discover how the proof identifies the Maulik-Okounkov Lie algebra with specific BPS Lie algebras. Understand the connection between these dimensional calculations and Kac's polynomials, which are used to count isomorphism classes of Q-representations over finite fields.