4:00–5:00 pm Ryerson 251, 1100 E. 58th St
Lecture 2: A knot invariant from grid diagrams
Knot Floer homology is an invariant for knots in three-space, defined by a suitable adaptation of Heegaard Floer homology. It has the form of a bigraded vector space, encoding information about the complexity of the knot, an enrichment (or “categorification”) of the Alexander polynomial. The invariant was originally defined in collaboration with Zoltan Szabo, and indepedently by Jacob Rasmussen. I will describe a purely combinatorial formulation of this invariant, discovered in joint work with Ciprian Manolescu and Sucharit Sarkar, and further elaborated in joint work with Manolescu, Szabo, and Dylan Thurston. I will also sketch some of the applications of this invariant to knot theory.