Knot Floer homology is a knot invariant that is defined using Heegaard diagrams to represent a knot inside a three-manifold and a version of Lagrangian Floer homology which counts so-called pseudo-holomorphic Whitney disks. A powerful invariant, knot Floer homology detects the genus and fiberedness of a knot, recovers the Alexander polynomial, and provides lower bounds on the unknotting number and four-ball genus of a knot.

Grid diagrams, which are combinatorial representations of a knot in the three-sphere, make it possible to define and prove the invariance of knot Floer homology without any analysis. I will discuss the construction of grid homology and give some examples. Speaker(s): Linh Truong (University of Michigan)