Fermionic Forms in Logarithmic Vertex Operator Algebras and BPS Quivers

Explore the intricate connections between quantum groups, vertex algebras, and quiver representations in this advanced mathematics lecture. Delve into the Kazhdan-Lusztig correspondence and examine how fermionic forms serve as a crucial link between different areas of representation theory. Trace the historical development of fermionic forms from rational VOAs to logarithmic VOAs, and discover their recent emergence in quiver representations related to enumerative geometry and curve counting. Gain insights into a new approach for constructing fermionic forms in broader families, bridging the gap between quivers and vertex algebras. This talk is part of the Workshop on Quantum Symmetries, focusing on tensor categories, topological quantum field theories, and vertex algebras.