Geometric Heegaard Floer theory for the combinatorially inclined

Please join us for a special two-part seminar on Geometric Heegaard Floer theory.

Since its introduction in the early 2000's, Heegaard Floer theory has had a tremendous influence on low-dimensional topology. This was first seen in its solutions to old problems (e.g., detecting knot genus), but the rich structures have since established themselves as objects of independent study. Early versions of the Heegaard Floer invariants were powerful, but extremely difficult to compute; today, some of the knot invariants can be defined via the completely combinatorial "grid homology". This has huge advantages for accessibility, but the underlying geometry is less apparent.

These talks will introduce a geometric perspective on Heegaard Floer invariants to an audience familiar with grid homology. While still suppressing many technical details, I'll try to provide context for where grid homology comes from, explain why it was such an exciting development, and indicate what its limitations still are.

Both talks will take place in the SMRI Seminar Room (A12 Room 301).

The first talk will be on Wednesday 11 September 3pm - 5pm.

The second talk will be on Thursday 12 September 10am - 12 noon.

If you are not familiar with grid homology, please still feel free to come along. If you would like to read a little about grid homology, a good reference is Grid Homology for Knots and Links by Peter S. Ozsvath, Andras I. Stipsicz, and Zoltan Szabo. In particular, chapters 3.1 and 3.2 introduce grid diagrams and chapter 4 introduces grid homology