# Trimester seminar series: Non-commutative motives and telescope-type problems

Derived representation theory plays an important role in the study of finite-dimensional algebras. In this speaker series we will pursue two distinct themes born out of this perspective: non-commutative motives and telescope-type problems. The speaker series will run between 1 October and 18 December and will consist of online talks given by invited speakers. There will be opportunities for informal discussion following the talks.

## Wednesday, December 16th, 3:30 p.m.

### Jacques Tits motivic measure

Speaker: Goncalo Tabuada (MIT)

#### Abstract

The Grothendieck ring of varieties, introduced in a letter from Grothendieck to Serre (August 16th 1964), plays an important role in algebraic geometry. In order to capture some of its flavor, a few motivic measures have been built (e.g., the counting motivic measure and the Euler characteristic motivic measure). In this talk I will present a new motivic measure, called the Jacques Tits motivic measure, and describe some of its numerous applications.

#### Zoom Login Data

https://uofglasgow.zoom.us/j/96928513353?pwd=bzA4Q3QvbUdLQXhxU0FTSjUrZTNDdz09

Meeting ID: 969 2851 3353

Passcode: 571350

## Wednesday, December 16th, 2 p.m.

### Krull-Gabriel dimension, m-dimension and Cantor-Bendixson rank in the Ziegler spectrum

Speaker: Mike Prest (Manchester)

#### Abstract

These dimensions are measures of complexity of definable categories of modules. I will describe them and the relations between them, using the functor categories approach. I will also touch on the relation with the powers of the radical of the category of finitely presented modules over an artin algebra.

#### Zoom Login Data

https://univr.zoom.us/j/83986782744?pwd=MFNIUlhKT01RZ2k4SzMydXNZUkJvQT09

Meeting ID: 839 8678 2744

Passcode: 870395

## Wednesday, November 18th, 2 p.m.

### The smashing spectrum of a valuation domain

Speaker: Jan Stovicek (Charles University, Prague)

#### Abstract

The derived categories of non-discrete valuation domains R seem to be a rare setting where the smashing localizations are fully classified despite the fact that telescope conjecture fails in general. I will explain this result from [1] along with the (unpublished) fact that the smashing localizations correspond to open sets of a spectral space Smash(R). For formal reasons, Spec(R) with the Thomason topology is a quotient space of Smash(R). I will illustrate the concept and the relation to Spec(R) on examples.

[1] S. Bazzoni, J. Šťovíček, Smashing localizations of rings of weak global dimension at most one, Adv. Math. 305 (2017).

#### Zoom Login Data

https://univr.zoom.us/j/85388708981?pwd=RTQvZzgwZXE0WXFnUStQSmYyS3hIdz09

Meeting ID: 853 8870 8981

Passcode: 005518

## Wednesday, October 21st, 2 p.m.

### Silting complexes over hereditary rings

Speaker: Lidia Angeleri Hügel (University of Verona)

#### Abstract

We will investigate parametrizations of compactly generated t-structures, or more generally, t-structures with a definable coaisle, in the unbounded derived category D(Mod-A) of a ring A. To this end, I will present a construction of t-structures from chains in the lattice of ring epimorphisms starting in A, which is a natural extension of the construction of compactly generated t-structures from chains of subsets of the Zariski spectrum known for the commutative noetherian case. I will also discuss constructions of silting and cosilting objects in D(Mod-A) which will lead us to some classification results over finite dimensional hereditary algebras. The talk will be based on joint work with Michal Hrbek.

#### Zoom Login Data

https://univr.zoom.us/j/82408089925

Meeting ID: 824 0808 9925

## Wednesday, October 7th, 2 p.m.

### Telescope conjecture and its variants in derived categories of commutative rings

Speaker: Michal Hrbek (Czech Academy of Sciences in Prague)

#### Abstract

We discuss some new developments concerning the validity of Telescope conjecture (TC) and its variants in the unbounded derived category of a commutative ring. Recently, a version of (TC) which applies to t-structures that are not necessarily stable was considered, with applications to the silting theory. This a priori stronger property of the derived category was recently shown to hold in many situations for which (TC) was already known to be true. We also demonstrate how the classification of compactly generated t-structures for commutative rings can be used to show that both (TC) and its non-stable variant can be checked locally with respect to localizations at maximal ideals of the Zariski spectrum.

#### Zoom Login Data

https://univr.zoom.us/j/81587695653

Meeting ID: 815 8769 5653