Knot homologies, Hilbert schemes, and Cherednik algebras

Workshop on Algebra and Representation Theory, Held on Oregonian Grounds

25 July - 29 July 2016
University of Oregon
Eugene, OR

The goal is this workshop to learn about the HOMFLY-PT homology of a closed n-strand braid, and to then explore some conjectural relations between this invariant, the Hilbert scheme of n points in the plane, and (in certain special cases) representations of Cherednik algebras, as initiated in:

Torus knots and the rational DAHA by Gorsky, Oblomkov, Rasmussen, and Shende

and subsequently developed by Gorsky, Hogancamp, and others.

The workshop will be led by Jacob Rasmussen, and will consist of a combination of lectures and problem sessions.
It will be organized by Ben Elias, under the watchful eye of Nicholas Proudfoot.

Logistics for Participants

General Schedule: There will be lectures and exercises Monday through Friday, from approximately 9AM to 5PM, with gaps between and a space for lunch. Wednesday is a half-day, with the afternoon being left open for an organized hiking trip to nearby Spencer Butte. Wednesday evening we will have a pizza party at a local park, sponsored by the workshop. On Monday, Tuesday, and Thursday evening there will be an optional, organized exercise session.

Food: Starting at 830AM each day of the workshop, coffee and pastries will be catered to the lecture room. Aside from this and the pizza party, participants will have to pay for their own food. Carson residence hall has a cafeteria with more substantial breakfast for purchase. There will be time to eat lunch at many local restaurants, and restaurant recommendations will be posted at a later date. Replace torus.html with restaurants.html above.

Accommodations: Participants will be staying in the Carson residence hall on campus. The cost of this will be covered by the workshop.

Accommodations and arrival/departure timing: It is assumed that participants will arrive in Eugene on Sunday before the workshop, and leave on either Friday night or Saturday after the workshop. Housing will be available for participants leaving on Sunday after the workshop as well, if necessary. Participants arriving earlier or leaving later should contact me for possible options, but housing is not guaranteed.

Accommodations and arrival: When you arrive, you need to check in at the Area Desk of the Living Learning Center, which is on 15th Avenue between University Street and Agate Street; there you will receive a key to your room. The confusing thing is that the building is disconnected (there is a South component and a North component). The component on 15th Avenue is the South component, but the component that contains the Area Desk is the North component (which is not bordered by any street at all). Also, if you arrive after 8pm, you will have to call this number: (541) 346-5686. When you depart, you will need to return your key to the Area Desk as well.

Transportation costs: Unless you have been told otherwise, we will not be covering any transportation costs.

Flying to Eugene: You should fly to the Eugene airport, code EUG. There are direct flights connecting Eugene to Seattle, Portland, Salt Lake City, Denver, San Francisco (often delayed!!), and Los Angeles. It is also possible to fly to Portland, which is a little over a two hour drive from Eugene - there are also shuttles and a train which can get you from Portland to Eugene, but this is typically far more complicated then just flying directly to Eugene.

Airport to Campus: There is no public transportation from the airport, so you'll have to take a cab, which should take about half an hour and cost about $30. Since a lot of you will be arriving around the same time, you might consider trying to find each other at the airport and sharing a cab. A webpage will be set up closer to the time of the conference to help coordinate this. Cabs back to the airport will be organized later in the conference.

Schedule, Lectures, and Exercises

See here.

Participant List

If you are on this list then I am expecting you to come to the workshop. Unless you have an asterisk by your name, accommodations will be provided to you.

Preliminary reading and exercises

Here are the two/three papers we picked as a baseline for everyone to read in advance. It would be great if people could learn about Khovanov homology, the Temperley-Lieb algebra and the Jones polynomial.

* Bar-Natan, On Khovanov's categorification of the Jones polynomial.
Read this lovely thing, up to the computational stuff.
* Jones, Hecke algebra representations of braid groups and link polynomials, on JSTOR, from Annals of Math.
Read Chapters 1-6 (although some of the nasty computations can be skipped)

Having accomplished this, we hope everyone will try to read:
* Cooper-Krushkal, Categorification of the Jones-Wenzl projectors.
Read Chapters 1-2, and if you're feeling ambitious, 3-4.

Some exercises to play with are here.
Additional suggestions for advance reading have been emailed to participants.


If you are interested in participating, email Ben. Please include your school, advisor, and a brief description of your research interests. Please place [WARTHOG] in the subject line of your email. Funding for accommodations in Eugene (but not for travel) will be available to students and postdocs as long as space and funds remain. Let Ben know if you have any special needs or requests.

Addendum: There has been an unprecedented show of interest in this workshop, and consequently space is now extremely limited (if you have not already asked, chances are it is too late). Still, it does not hurt to ask.