Masterclass on Higher Representation Theory
University of Copenhagen, 6 - 17 March 2023
The study of representations of groups in the setting of stable infinity-categories might loosely be termed as “higher representation theory”. Some natural questions include the possibility of splitting these representation categories and what the representation rings (or in more modern terms, the algebraic K-theory ring spectrum) of these stable categories look like. As infinity-categorical methods approach their next level of maturation, such investigations have seen a flurry of interesting developments in recent years. The aim of the masterclass is, therefore, to expose various strands of this exciting progress, and the main streams of topics to feature will include categorified Smith theory, defect bases of stable representation categories, descent on equivariant algebraic K-theory via nilpotence, Picard groups of spectral representations, and various guises and appearances of the Tate construction.
The lectures should be accessible to master’s and graduate students, and the techniques and results discussed therein should be of interest to mathematicians working or hoping to work in (equivariant) stable homotopy theory, algebraic K-theory, and representation theory. The overall goal is to serve as an invitation to this beautiful constellation of themes by providing a platform not just to communicate the fundamental results and techniques, but also to narrate important programs and conjectures as an invitation for further work in this field.
The masterclass will be divided into two weeks which can be attended independently. Both weeks will consist of one main lecture series each and these lectures will be accompanied and augmented by exercise sessions and many supporting lectures exploring connections to closely related areas of current research given by speakers including Robert Burklund (Copenhagen), Lennart Meier (Utrecht), Lior Yanovski (Jerusalem) and Tobias Barthel (Bonn). The speakers for the main lecture series are:
- Week 1 [6-10 Mar]: David Treumann (Boston)
- Week 2 [13-17 Mar]: Akhil Mathew (Chicago)
You can find the abstracts here
Week 1
Speakers: Tobias Barthel (Bonn), Lennart Meier (Utrecht), David Treumann (Boston)
| Monday | Tuesday | Wednesday | Thursday | Friday |
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09:30-10:00 Registrations |
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10:15-11:15 Treumann-1 Aud 6 |
10:15-11:15 Meier-3 AKB, Aud 3 |
10:15-11:15 Exercise-4 419/420 |
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11:15 -11:45 Coffee |
11:15 -11:45 Coffee |
11:15 -11:45 Coffee |
11:15 -11:45 Coffee |
11:15 -11:45 Coffee |
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11:45-12:45 Meier-1 Aud 6 |
12:00-13:00 Meier-2 AKB Aud 1 |
12:00-13:00 Treumann-2 Aud 3 |
11:45-12:45 Treumann - 4 Aud 5 |
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Lunch |
Lunch |
Lunch |
Lunch |
Lunch |
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14:15-15:15 Exercise-1 419/420 |
14:15-15:15 Exercise-3 419/420 |
14:15-15:15 Treumann -3 Aud 3 |
14:15 - 15:15 Treumann - 5 Aud 3 |
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15:15 -16:15 Treumann Algebra and Topology Seminar Aud 1 |
Coffee |
Coffee |
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| Break |
15:45-16:45 Grodal Aud 3 |
15:45 -16:45 Exercise -5 Aud 3 |
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17:00 Pizza |
16:30 -17:30 Exercise 2 Aud 1 |
16 30 Drinks 419/420 |
Week 2
Speakers: Robert Burklund (Copenhagen), Akhil Mathew (Chicago), Lior Yanovski (Jerusalem)
| Monday | Tuesday | Wednesday | Thursday | Friday |
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09:30-10:00 Registrations |
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10:30-11:30 Burklund-1 StUp1, DIKU |
10:15-11:15 Exercise StUp 1, DIKU |
10:15-11:15 Exercise 419/420 |
10:15-11:15 Mathew-4 StUp 1, DIKU |
10:15-11:15 Mathew-5 Aud 2 |
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11:30 -12:00 Coffee |
11:15 -11:45 Coffee |
11:15 -11:45 Coffee |
11:15 -11:45 Coffee |
11:15 -11:45 Coffee |
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12:00-13:00 Lunch |
12:00-13:00 |
12:00-13:00 Mathew - 2 Aud 2 |
11:45-12:45 Yanovski -3 St Up 1 |
11:45-12:45 Exercise Aud 2 |
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Lunch |
Lunch |
Lunch |
Lunch |
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14:15-15:15 |
14:15-15:15 Mathew-1 StUp 1, DIKU |
14:15-15:15 Burklund -2 Aud 2 |
14:15-15:15 Burklund -3 STUp 1, DIKU |
14:15 - 15:15 |
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15:15 -16:15 Yanovski -1 AKB Aud 1 |
Coffee |
Coffee |
Coffee |
Coffee |
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15:45-16:45 Yanovski -2 StUp 1, DIKU |
15:45-16:45 Mathew 3 Aud 2 |
15:45-16:45 Exercise StUp 1, DIKU |
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17:00 Pizza |
Conference Dinner |
The conference/masterclass will take place at the Department of Mathematical Sciences, University of Copenhagen. See detailed instructions on how to reach Copenhagen and the conference venue.
Tickets and passes for public transportation can be bought at the Copenhagen Airport and every train or metro station. You can find the DSB ticket office on your right-hand side as soon as you come out of the arrival area of the airport. DSB has an agreement with 7-Eleven, so many of their shops double as selling points for public transportation.
A journey planner in English is available.
More information on the "find us" webpage.
We kindly ask the participants to arrange their own accommodation.
We recommend Hotel 9 Små Hjem, which is pleasant and inexpensive and offers rooms with a kitchen. Other inexpensive alternatives are CabInn, which has several locations in Copenhagen: the Hotel City (close to Tivoli), Hotel Scandinavia (Frederiksberg, close to the lakes), and Hotel Express (Frederiksberg) are the most convenient locations; the latter two are 2.5-3 km from the math department. Somewhat more expensive – and still recommended – options are Hotel Nora and Ibsen's Hotel.
An additional option is to combine a stay at the CabInn Metro Hotel with a pass for Copenhagen public transportation (efficient and reliable). See information about tickets & prices.
Limited funding is available, and the interested applicant should register by 17 February 2023 if they would like to be considered for financial support; otherwise, the deadline for general registrations is 27 February 2023. Note that we cannot, unfortunately, guarantee said funding for every applicant.
The registration is now closed. Please contact Vignesh Subramanian for more queries.
