Hypertoric varieties and Koszul duality April 4, 2008
Posted by Ben Webster in Algebraic Geometry, category O, combinatorics, D-modules, homological algebra, IAS, representation theory, talks.trackback
So, on Wednesday, I gave a talk with the above title at IAS, about work in progress with Tom Braden, Tony Licata, and Nick Proudfoot. I was hoping to get David Nadler to blog it for me, but he was *ahem* indisposed. Failing that, I’ll direct you all to David Ben-Zvi’s notes (warning: freaking huge PDF). Hopefully, that will whet your appetite for the forthcoming paper.
oh that’s sad. I was looking forward to David’s liveblogging.
Let me also advertise my set of notes on the same subject, which have the advantage of not being hand written by BZ:
http://www.uoregon.edu/~njp/sd.pdf
first let me say I have much smaller tiff files for those who like
them (should I be putting those online in addition? not sure
how popular those are).
Since Navid Zadler was indisposed let me comment that the talk KICKED ASS.
Besides the charming Webster wit and attitude for which
this blog is such an excellent showcase, the math was also top notch.
Besides having intrinsically fascinating results,
it seems that Tom, Tony, Nick and Ben are on the cutting
edge of the next “mirror symmetry” revolution.
Intrilligator and Seiberg
introduced an analogue of mirror symmetry for
THREE-dimensional (N=4) superconformal field theories, which has
yet to have the huge mathematical impact it is bound to have.
Gaiotto and Witten are using it to understand the universe
(by which I mean in particular Langlands functoriality – see some of my Witten lecture notes if you can stomach the handwriting and filesize), and
this gang have found it independently and can
teach the physicists a thing or two about it as well – this
physical duality is still very mysterious (since it involves
flowing understood theories to their ill-understood conformal
limits) and so the math can provide a guiding light.
Exciting times!
Wow. After a glowing testimonial like that, I feel I should add: I’m available for birthdays, weddings, AND bar mitzvahs.
Thanks for those pdf notes! Is the Cayley graph for the Deligne groupoid of the triangle right? It looks like it has an extra double edge.
Yeah, you’re right. The vertical edges connecting the top node to the center one shouldn’t be there.