Explore a lecture from the Unni Namboodiri Lectures in Geometry and Topology series featuring Princeton's Peter Ozsvath discussing Knot Floer homology, an invariant for knots in three-space. Learn how this bigraded vector space encodes information about knot complexity and serves as a categorification of the Alexander polynomial. Discover the purely combinatorial formulation of this invariant developed through collaborative work with Ciprian Manolescu, Sucharit Sarkar, Zoltan Szabo, and Dylan Thurston. The lecture also covers applications of Knot Floer homology to broader knot theory, providing insights into this specialized area of topology presented by the University of Chicago Department of Mathematics.