Grid homology summer course

June 16th further thoughts:

For those interested in more on grid diagrams, see this remarkable paper by Dynnikov. Marc Culler implemented Dynnikov's algorithm. It's fun to play with his program gridlink

Grid diagrams fit into the bigger picture of Legendrian knots. For more on this, see Chapter 12 of the book. Here is a nice reference on Legendrian knots.

Knot homology detects the unknot. This has the following pretty concrete manifestation: the homology of GH-tilde of a grid diagram has rank 2^(n-1) if and only if the grid represents the unknot. Here's an open question: Does this have a purely grid-diagrammatic proof?

Grid homology can be defined over Z rather than Z/2 (this is done in Chapter 15. Here's an open question: does grid homology ever have torsion? (We don't know of any examples!)