| We will start by discussing grid diagrams for knots, and a definition of the Alexander polynomial in terms of grid diagrams. From there we will give the (one year old) combinatorial definition of knot Floer homology, due to Manolescu-Ozsvath-Sarkar. We will then discuss how this definition might be extended to braids (or tangles?). Time permitting, we will conclude with a discussion of the symplectic geometry which led to the combinatorics. At least the first three quarters of the talk should require little background in the area; the second half is work in progress of P. Ozsvath, D. Thurston and the speaker. |
