Coherent-constructible equivalences in local Geometric Langlands and Representation Theory

Workshop on Algebra and Representation Theory, Held on Oregonian Grounds

July 22-26, 2024
University of Oregon
Eugene, OR

The goal of this workshop will be to introduce the participants to the construction of a series of equivalences of categories due to Bezrukavnikov (in collaboration with various people) motivated by the local Geometric Langlands program, culminating in [B2], and which have found important applications in Representation Theory (see e.g. [B1]). The starting point of these constructions is the Geometric Satake Equivalence, which describes the category of (algebraic) representations of a connected reductive algebraic group in terms of perverse sheaves on the affine Grassmannian of the Langlands dual group, see [MV]. One can then consider various (derived) categories of constructible sheaves containing the latter category, and try to describe them in terms of the dual group, which usually involves coherent sheaves.

In practice, we will start by explaining the constructions of the derived categories of constructible or coherent sheaves on varieties, and the various functors that can be used to work with them. Then we will review the construction of the Geometric Satake Equivalence, and finish by discussing the construction of the equivalences in [AB] and (if time permits) in [B2].

The workshop will be led by Pramod Achar and Gurbir Dhillon and Simon Riche, 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. In 2024 it is supported by NSF grant DMS-2039316.

Background reading

If you're interested in attending WARTHOG, please read this page for information on expected background for the workshop, together with suggested readings and other references.

Schedule, Exercises, and Lecture Notes

Please follow this link to see the schedule of lectures. Exercises and lecture notes for each lecture will be posted there after each lecture.

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 (+ salads) party at a local park, sponsored by the workshop. On Monday, Tuesday, and Thursday evening there may be an optional exercise hangout in the evening.

Our typical daily routine is: hour of lecture, 45 minutes of exercise, 15 minute break, repeat four times, with a longer break for lunch.

Food: Starting at 830AM each day of the workshop, coffee and bagels and fruit will be catered to the lecture room. Aside from this and the pizza party, participants will have to pay for their own food. Several nearby residence halls have a cafeteria with more substantial breakfast for purchase, and there are many restaurants in the EMU (student center). There will be time to eat lunch at many local restaurants.

Accommodations: Participants will be staying in a dormitory on campus, in single occupancy rooms which have both shared bathrooms and single-occupancy gender-neutral bathrooms. Linens and towels are provided. The cost of this will be covered by the workshop. Details will be emailed shortly before arrival. Participants with special accommodation needs are encouraged to email Ben.

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. Participants arriving earlier or leaving later should contact me for possible options, but housing is not guaranteed.

Transportation costs: Unless you have been told otherwise, we will not be covering your transportation costs. However, if other options have not availed you, please do email me (Ben Elias) and we can discuss options. We have funds to cover travel for a decent number of participants, but not for everyone. If we do end up covering your transportation, make sure to fly to EUG during the expected dates, or contact me to discuss price comparisons.

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, Los Angeles, and recently Chicago. In my personal experience, if you fly through San Francisco then your flight will be delayed and you will miss your connection, so try to find another option if possible. It is also possible to fly to Portland, which is a little over a two hour drive from Eugene - there are shuttles and a train which can get you from Portland to Eugene and back, but this is typically 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 or a shuttle, which should take about twenty minutes and cost about $30. Cabs in Eugene are run by a host of private companies, some better than others. Avoid Oregon Taxi if you can. If the driver asks which route to take, just say to take 99. You might want to try this new shuttle service.

Getting around: During the conference you will be able to walk everywhere you need to go. If you are staying longer in Eugene or in Oregon for recreational purposes, it is easy to rent a bicycle, and car rentals (within the city, not from the airport) are decently priced.


For the first time ever, WARTHOG is full! If you wish to be added to the waitlist, please follow the instructions for registering below.

If you are interested in participating, email Ben Elias. Please include your school, advisor, and a brief description of your research interests. Funding for accommodations in Eugene (but not for travel) will be available to students and postdocs as long as space remains. Limited funds are available for travel upon request, primarily for US citizens or permanent residents.

This is not a final confirmation of attendance, which will be requested at a later date.