# Seminars in Algebra (Fall 2023)

Here are a few notes about our algebra seminar this semester:

- Talks will be about 45 minutes, with time for questions afterwards.

If you have any questions or comments about the seminar, please contact Mads Sandøy or Laertis Vaso.

## Upcoming seminar talks

(Previous talks can be found below and by clicking on the menu on the left.)

## Tuesday, March 12th, 2024, at 14:15 in room 656 (Simastuen), SBII

**Speaker:** Håvard Utne Terland
(NTNU)

**Title**: TBA

**Abstract:** TBA

## Spring 2024 seminar talks

## Wednesday, January 17th, 2024, at 13:00 in room 656 (Simastuen), SBII

**Speaker:** Claire Amiot (Institut Fourier)

**Title**: Linear Invariants for poset representations

**Abstract:** Let \(P\) be a poset. An \(\mathbb Z\)-invariant on \(\rm mod P\) is a \(\mathbb Z\)-linear map \(K_0^{\rm sp}(\rm mod P)\to \mathbb Z^N\). In this talk, I will discuss several examples of invariants that appear in persistence theory coming either from relative exact structures or from order embeddings. This is a joint work with Thomas Brüstle and Eric Hanson.

## Monday, January 22th, 2024, at 11:00 in room 656 (Simastuen), SBII

**Speaker:** Dag Oskar Madsen (Nord universitet)

**Title**: The classification of Higher Auslander algebras among Nakayama algebras

**Abstract:** Together with Marczinzik and Zaimi we proved that for any \(n \leq r \leq 2n-2\) there exists a unique Nakayama algebra with \(n\) vertices and global dimension \(r\) that is a higher Auslander algebra. In this talk I will discuss this result and progress made by other authors in the more complicated case \(r < n\).

## Tuesday, February 13th, 2024, at 14:15 in room 656 (Simastuen), SBII

**Speaker:** Endre Sørmo Rundsveen (NTNU)

**Title**: \(\tau_d\)-tilting theory for Nakayama Algebras

**Abstract:** Tilting theory has been a great tool in representation theory since its inception in the 1970’s. It was generalized to the concept of support \(\tau\)-tilting in 2014, closing a gap introduced by mutation, and providing a bijection with functorially finite torsion classes. In higher AR-theory there has recently been several proposed generalization of support \(\tau\)-tilting (see e.g. Jacobsen-Jørgensen, Martínez–Mendoza and Zhou–Zu) with differing points of departure. In this talk our point of departure is in the generalization of torsion classes to \(d\)-torsion classes.

In ongoing work August, Haugland et.al. have shown that functorially finite torsion classes can be injectively sent to what we call strongly maximal \(\tau_d\)-tilting pairs. The aim of the talk is to classify these for truncated (acyclic) Nakayama Algebras when \(d>2\) or \(l=2\). Despite having a different point of origin, we also show that there is a clear relationship between strongly maximal \(\tau_d\)-tilting pairs and the \(\tau_d\)-tilting modules investigated by Martínez–Mendoza through \((d+1)\)-silting complexes. This is joint work with Laertis Vaso.

## Tuesday, February 27th, 2024, at 14:15 in room 656 (Simastuen), SBII

**Speaker:** Jacob Fjeld Grevstad (NTNU)

**Title**: Derived representation type and G-equivariant spectra

**Abstract:** The problem of classifying indecomposable representations is one of the earliest problems in representation theory. The famous Tame-Wild dichotomy loosely says that algebras split into two groups: those where classifying modules are relatively easily, and those where a classification is completely hopeless. In 2003 a similar dichotomy was proven for perfect complexes in the derived category.

There is a close relationship between the homotopy category of G-equivariant spectra and the derived category of cohomological MacKey functors. In this talk we look at which groups give rise to derived tame and which give rise to derived wild cohomological MacKey functors.

(Joint work in progress w/ Clover May)