Infinite-dimensional methods in commutative algebra

Workshop on Algebra and Representation Theory, Held on Oregonian Grounds

June 26-30, 2022
University of Oregon
Eugene, OR

In the last several years, a variety of new infinite dimensional tools have been introduced in algebra and geometry, such as twisted commutative algebras, and varieties of tensors in infinitely many variables. After introducing these tools, we will discuss their applications to a wide variety of fields, focusing on their applications within commutative algebra.

Update: the workshop will likely focus on two main themes. First, the proof of Stillman's conjecture using ultraproducts. Second, the study of GL-varieties (infinite-dimensional varieties with an action of the infinite general linear group), and using them to give a second proof of Stillman's conjecture. More details on the material covered in the workshop will become available in the upcoming weeks.

The workshop will be led by Andrew Snowden, 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.

Background reading

If you plan to attend WARTHOG, please read this page which describes the background we expect you to acquire before the workshop begins. The link also contains many helpful references.

Schedule, Exercises, and Notes

Please follow this link to see the schedule of lectures. Exercises and Lecture Notes can also be found from that link, and will be posted after the relevant lecture.


If you are interested in participating, email Ben Elias. 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 commonly for travel, see below) 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.

Logistics for Participants

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

Accommodations: Participants will be staying in Earl Hall on campus, in single occupancy rooms which have both shared bathrooms and single-occupancy gender-neutral bathrooms. 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 Saturday before the workshop, and leave on either Thursday night or Friday after the workshop. This year we can not offer any housing for Friday night, due to a university policy. Participants arriving earlier or leaving later should contact me for possible options, but housing is not guaranteed.

Arrival procedure: Check-in for housing is at the Service Desk at Global Scholars Hall. If you're arriving after 9PM, please call their number 541-346-9114 to check in.

Transportation costs: Unless you have been told otherwise, we will not be covering your transportation costs. If other options have not availed you, please email me (Ben Elias) and we can discuss options. (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.)

Transportation costs and Covid: We don't expect to have to cancel the event because of coronavirus, but one can never be sure. We are unable to reimburse you for expenses in the event of cancellation, so please take reasonable precautions.

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, 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, 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 they ask which route to take, just say to take 99. 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 google group 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.

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 very cheap.

What about Coronavirus?

We will be developing a covid plan approved by the University of Oregon in due course. We can all cross our fingers and hope that the situation in June is better than it is today.

Here's what I know so far. Anyone attending the conference or staying in University housing will need to either be vaccinated to take frequent covid tests. In the event that a participant needs to isolate and quarantine, participants will not be allowed to quarantine in University housing, so we will assist in finding other housing.

Please, please, take a test before you travel to Eugene! You'll be much happier if you must quarantine at home.