Quantum Algebra/Quantum Topology Seminar - Aaron Lauda

Abstract: The Alexander polynomial for knots and links can be interpreted as a quantum knot invariant associated with the quantum group of the Lie superalgebra gl(1|1). This polynomial has been famously categorified to a link homology theory, knot Floer homology, defined within the theory of Heegaard-Floer homology. Andy Manion showed that the Ozsvath-Szabo algebras used to efficiently compute knot Floer homology categorify certain tensor products of gl(1|1) representations. For representation theorists, work of Sartori provides a different categorification of these same tensors products using subquotients of BGG category O. In this talk we will explain joint work with Andy Manion establishing a direct relationship between these two constructions. Given the radically different nature of these two approaches, transporting ideas between them provides a new perspective and allows for results that would not have been apparent otherwise, including a surprising connection between Ozsvath-Szabo theory and hypertoric varieties.