# Workshop: Spectral methods in equivariant mathematics

**Dates: **October 24 - 28, 2022**Venue:** HIM lecture hall, Poppelsdorfer Allee 45, Bonn

Organizers: John Greenlees (Warwick), Jesper Grodal (Copenhagen), Radha Kessar (London), Henning Krause (Bielefeld)

Speakers:

- Robert Burklund (Copenhagen)
- Natalia Castellana (Barcelona)
- Ivo Dell’Ambrogio (Lille
- Martin Gallauer (Bonn)
- Paul Goerss (Evanston)
- Sira Gratz (Aarhus)
- Markus Hausmann (Stockholm)
- Kaif Hilman (Copenhagen)
- Magdalena Kedziorek (Nijmegen)
- Bernhard Keller (Paris)
- Achim Krause (Münster)
- Nick Kuhn (Charlottesville)
- Markus Linckelmann (London)
- Nadia Mazza (Lancaster)
- Amnon Neeman (Canberra)
- Luca Pol (Regensburg)
- Catharina Stroppel (Bonn)
- Peter Symonds (Manchester)

**Description:**

The workshop focuses on aspects of spectral geometry in which group actions play a significant role, and we have taken an inclusive attitude both to the objects considered and the groups that act on them. It therefore includes representation theory of groups, manifolds with group action, fields with Galois groups acting, equivariant cohomology theories and the categorical structures associated to change of groups. As for the groups, they may be finite or infinite, discrete, profinite, continuous, smooth, global or generic.

The workshop will gather together mathematicians from many fields to benefit from the range and richness this brings, to encourage interaction between participants from different fields, and to build connections between different research areas. Speakers are encouraged to make their talks accessible to newcomers to the field, both established mathematicians and early career researchers.

The format is also designed to give time for discussion with four plenary talks per day except on Wednesday where the afternoon will be free and there will be three talks in the morning.

As one way to start conversations we will have a Gong Show on Monday afternoon: participants at any career stage can volunteer to use one of the very short slots to describe a problem or a result and thereby begin conversations during the rest of the week.

Click here for the schedule.

Click here for the abstracts.

Trimester Program guests, who were invited and have confirmed to be at HIM during the period of this workshop, are eligible to attend this event.

# Video Recordings

# Day 1

Nick Kuhn: Chromatic fixed point theory

Catharina Stroppel: Ext and endomorphism algebras motivated by Fukaya categories

Natalia Castellana: Cosupport and costratification in tt-geometry

Markus Hausmann: Invariant prime ideals in equivariant Lazard rings

# Day 2

Luca Pol: Classifying separable algebras via Galois theory

Magdalena Kedziorek: Uniqueness of rational equivariant K-theory

Kaif Hilman: Multiplicative norms on equivariant algebraic K-theory

# Day 3

Nadia Mazza: On endotrivial modules

Ivo Dell'Ambrogio: Equivariant tensor triangulated categories of C*-algebras

Paul Goerss: J-homomorphisms and Picard Groups

# Day 4

Amnon Neeman: Vanishing negative K-theory and bounded t-structures

Achim Krause: Integral endotrivial modules

Sira Gratz: Invariants of bounded and perfect complexes

# Day 5

Bernhard Keller: On the Donovan-Wemyss conjecture, after Wemyss, Jasso-Muro and others

Peter Symonds: The module structure of a groupt action on a ring

Robert Burklund: The Balmer spectrum of cellular C-motivic spectra