In what may be a first in the math blogosphere I will be liveblogging Ben’s talk. Until the appearance of math vlogging I think this puts us at the cutting edge of math blogging technology. In the absense of heckling I will be keeping track of how often Ben says “perverse sheaves” and “equavariant cohomology of a point.”
(3:40) Some excitement, Ben’s computer threatens to die during the talk. Dylan’s power adapter saves the day. We also have our first laugh line: “Soergel bimodules have 3 definitions, some of you may like some more than the others, some of you may not like any of them.”
(3:50) We’re all the way through two slides and we’ve only had one mention each of “perverse sheaves” and “derived category.” There have been 5 questions, as long as the number of questions beats out the number of mentions of “perverse sheaves” things are good.
(3:55) Ben’s prepared some fancy technology: a little button saying “what?” that let’s him insert a slide on equivarient cohomology. We’re definitely taking the cohomology of a point now. I must admit I’ve always found that very confusing.
(4:02) We’re back in “Soergel-land” and the audience is still peppering Ben with questions.
(4:05) Ben is always saying he forgets what mistakes people pointed out during the talk, so, on slide 8 fix the gradings. Update: also add the “t-invariants” somewhere in the midteens.
(4:08) Urs asks in comments why we care about Soergel bimodules. Some people care because they like the BGG category O. At this conference they care because of Khovanov-Rozansky’s HOMFLY homology. The basic idea is that the Jones polynomial comes from certain nice traces on the tower of Hecke algebras. HOMFLY homology comes from a categorification of this picture. Soergel bimodules categorify the Hecke algebra (that is they are a category whose split Grothendieck group is the Hecke algebra) and Hochschild homology categorifies the Jones-Ocneanu trace. Using Rouquier’s categorification of the map from the braid group to the Hecke algebra this categorified trace gives HOMFLY homology.
(4:25) This talk is much more exciting than the last time I saw it. Apparently Jake Rasmussen’s talk included a seemingly innocuous result that suddenly makes Ben and Geordie’s results hold far more generally.
(4:31) Apparently when Ben gets an email it appears on the screen. Maybe I’ll send him one during the questions.
(4:33) Ben hits the summary right on time at 4:29 on the lecture hall clock (my computer is 4 minutes faster).
(4:37) Nice question: What is the categorification of the Jones-Wenzl idempotents?
(4:43) Signing off, great conference! I may have some posts on some earlier talks that we haven’t dicussed yet. There was a lot of interesting stuff. Jorgen is telling us to publicise the open position at CTQM. Tell your topologist friends!