# Workshop: Spectra, triangles, and higher structures

**Dates: **December 05 - 09, 2022**Venue:** HIM lecture hall, Poppelsdorfer Allee 45, Bonn

Organizers:

Paul Balmer (UCLA), Tobias Barthel (Bonn), Paul Goerss (Northwestern), Markus Linckelmann (London), Julia Pevtsova (UW)

Click here for the schedule.

Click here for the abstracts.

Speakers:

Tom Bachmann (Oslo)

Scott Balchin (Bonn)

Benjamin Briggs (Berkeley)

Merlin Christ (Hamburg)

Pavel Etingof (Boston)

David Gepner (Johns Hopkins)

Jesper Grodal (Copenhagen)

Jeremiah Heller (Urbana-Champaign)

Mike Hill (Los Angeles)

Srikanth Iyengar (Utah)

Radha Kessar (Manchester)

Janina Letz (Bielefeld)

Cris Negron (Los Angeles)

Beren Sanders (Santa Cruz)

Sarah Scherotzke (Luxemburg)

Vesna Stojanoska (Urbana-Champaign)

Kent Vashaw (Boston)

Alexandra Zvonareva (Stuttgart)

**Description:**

The related concepts of infinity-categories and tensor triangulated categories have many antecedents and core examples in algebraic topology, algebraic geometry, and representation theory. These include categories built from sheaves, from group representations, from classical spectra in spaces, and all the ways these ideas can be mixed and matched. The last fifteen years have seen the emergence of new fields where these ideas apply, the extension of classical ideas to these new areas, the revelation of unexpected new structures, an explosion of new techniques, and applications to unexpected areas of mathematics quite a long way from the roots.

The aim of this workshop is to build on these developments and to highlight recent new results. This will include lectures in derived algebraic geometry, motivic homotopy theory, tensor-triangular geometry in its various guises, representation theory, and related areas of commutative algebra, algebraic models, functor categories, and stable module category theory. We hope to emphasize the connections between these lines of thought, to highlight the ways in which old problems led to new ideas, and to see how the new directions in turn shed new light on the classical problems.

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

Mike Hill: Equivariant commutative ring spectra

Scott Balchin: The local(e)-to-global principle

Beren Sanders: Costratification in tensor triangular geometry

Srikanth Iyengar: Local dualisable objects

# Day 2

Janina Letz: Homotopical characterization of exceptional complete intersection maps

Alexandra Zvonareva: Derived equivalences of Brauer graph algebras & the action of spherical twists

Tom Bachmann: Motivic real étale homotopy theory revisited

# Day 3

Benjamin Briggs: Syzigies of the cotangent complex

Radha Kessar: Weight theory beyond finite groups

# Day 4

Jeremiah Heller: Power operations and normed spectra

Kent Vashaw: On the spectrum and support theory of a finite tensor category

Merlin Christ: Perverse schobers and representation theory

# Day 5

Jesper Grodal: String topology of finite groups of Lie type

Vesna Stojanoska: Deforming representations of the Morava stabilizer group

Cris Negron: Some derived geometry for the Taft algebra

Pavel Etingof: Lie theory in tensor categories with applications to modular representation theory