Quivers, Curve Counting, and Fermionic Sums in Topology

Explore the intricate connections between quantum groups, vertex algebras, and enumerative geometry in this advanced mathematics lecture. Delve into the Kazhdan-Lusztig correspondence and its relation to fermionic forms, which serve as a crucial link between graded dimensions of VOA representations and braiding data. Trace the historical development of fermionic forms from rational VOAs in the 1980s to logarithmic VOAs in recent decades. Discover how similar structures have emerged independently in quiver representations within enumerative geometry and curve counting. Examine the newly established bridge between quivers and vertex algebras, gaining insights into fermionic forms and learning about a novel method for writing these forms in expanded families. This talk, part of the "Geometry, Topology, Group Actions, and Singularities in the Americas" conference, offers a deep dive into cutting-edge mathematical concepts at the intersection of algebraic topology, algebraic geometry, and mathematical physics.