# Special Year Seminar 2020-21 on Geometric and Modular Representation Theory

This is the seminar website for the 2020-2021 IAS Special Year.

## Information

At least for the first semester, we will be mostly holding "hybrid seminars," with talks on Zoom but some members participating locally.

• Time: Wednesdays 3-5pm or 7-9am (Princeton time)
• Location: Zoom and (starting 9/30) Simonyi 101

We will hold the Princeton time constant. Please note that daylight savings may affect the meeting time in your location.

### Speaking slots

We have reserved three slots for this seminar: Wednesdays 7-9am, Wednesdays 3-5pm, and Thursdays 7-9am. The first two are speaking slots, and the speaker may decide (based on their timezone) which slot they prefer. Then those that cannot make it meet in the next slot to watch a recording of the seminar and discuss.

So, on any given week, we will do either of the following:

• The seminar takes place on Wednesday 3-5pm. Those who can't attend it watch the recording together on Thursday 7-9am.
• The seminar takes place on Wednesday 7-9am. Those who can't attend it watch the recording together on Wednesday 3-5pm.

The schedule of talks below shows the speaking slot.

### For speakers

IAS announces the talks for the upcoming week each Friday. Please send your title and abstract to Shotaro Makisumi by Tuesday before that, e.g. for the talk on Sep 9th, we would like your title/abstract by Sep 1st. Speakers should also send the talk notes so that they can be posted here before the talk.

### Seminar format

Our seminar is reserved for 2 hours each week, but we expect each meeting to run closer to one hour than to two. We will adopt the following structure:

• The first hour will be the talk itself, broken down as follows: 25 minutes, 5 min break, 25 minutes, 5 min break.
• The second hour starts with questions, followed by discussion, and finally a truly optional extra 25 min of talk if necessary.

### Participation guidelines

We may change these depending on how things go.

• You will be muted by default.
• All members are encouraged if possible to have their video on. This makes it much easier for the speaker to see what is being followed, and encourages audience participation.
• To ask questions, you can do either of the following:
• First type your question in the chat. Anyone in the audience is welcome to answer these questions. If questions are unresolved after some time, the organizer will stop the speaker, and then you can unmute yourself and ask the question.
• Unmute yourself and ask the question directly.

## Schedule of talks and notes

Abstracts can be found further down the page.

Fall Semester

Date Speaker Title Slot Video Notes
Sep 9 Jay Taylor Broué's abelian defect group conjecture, I W3-5pm IAS .pdf
Sep 16 Daniel Juteau Broué's abelian defect group conjecture, II W3-5pm IAS .pdf
Sep 23 No talk Week of postdoc talks
Sep 30 Raphaël Rouquier Broué’s abelian defect group conjecture, III W3-5pm .pdf
Oct 7 TBD TBD TBD IAS
Oct 14 TBD TBD TBD IAS
Oct 21 TBD TBD TBD IAS
Oct 28 TBD TBD TBD IAS
Nov 4 TBD TBD TBD IAS
Nov 11 TBD TBD TBD IAS
Nov 18 TBD TBD TBD IAS
Nov 25 TBD TBD TBD IAS
Dec 2 TBD TBD TBD IAS
Dec 9 TBD TBD TBD IAS
Dec 16 TBD TBD TBD IAS

## Abstracts

September 9: Broué's abelian defect group conjecture, I by Jay Taylor (USC)

Abstract: This talk will form part of a series of three talks focusing on Broué’s Abelian Defect Group Conjecture, which concerns the modular representation theory of finite groups. We will pay particular attention here to the ‘geometric’ form of the conjecture which concerns finite reductive groups such as $GL_n(q)$ and $SL_n(q)$. Broué’s conjecture gives a strong structural reason for many numerical coincidences one sees amongst characters and is part of a general ‘local/global phenomena’ that is abundant in the theory.

In this first talk we will briefly recall the necessary background material, get to the point where we can state the conjecture, and discuss some important examples.

September 16: Broué's abelian defect group conjecture, II by Daniel Juteau (CNRS / Université de Paris)

Abstract: In this second talk about Broué’s Abelian Defect Group Conjecture, we will explain its geometric version in the case of finite groups of Lie type: the equivalence should be induced by the cohomology complex of Deligne-Lusztig varieties. This was actually the main motivation for the conjecture in the first place. We will illustrate those ideas with the case of SL(2,q).

September 30: Broué’s abelian defect group conjecture, III by Raphaël Rouquier (UCLA)

Abstract: TBD

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