So, I’m stuck in the Eugene airport for a few hours (the good news is that they have free wireless), due to weather in San Francisco (why a person going from Oregon to Boston would go through San Francisco, I’m not sure, but perhaps United Airlines can tell you). I’m finally done (assuming I actually get home today), with a crazy month of travelling, which included 6 different talks in 6 different places (admittedly in only 4 different cities). Of course, this lead to me putting my energies into making Beamer slides instead of writing posts (or papers), so I thought I would point any interested parties to said slides, which are now posted on my website.
The most recent ones are from a colloquium at the University of Oregon, with some generalities on knot homology and categorification, and then my thoughts on how to categorify Reshetikhin-Turaev knot invariants (this is still conjectural at the moment, but I think we’re getting closer).
Before that, I gave a talk at the University of Bonn (like I said, it was a crazy month) on the conjectures I’ve been working on with Braden, Licata and Proudfoot about symplectic duality. This is somewhat similar content to my MIT symplectic seminar talk, but with a much more algebraic focus (I think it was also a better structured talk, since I learned from some of my mistakes, but maybe that won’t come through just looking at the slides).
Even earlier, I gave a short talk at Knots in Washington about my work with Geordie Williamson on colored HOMFLYPT homology. This is an interesting story, in that this knot invariant has given a purely algebraic definition by Mackaay, Stosic and Vaz, but they haven’t given a proof of invariance, or that you get the right decategorification. Geordie and I have come up with a geometric description that allows you to prove invariance and decategorification. The paper is coming soon, I promise.