Laboratoire d'informatique de l'École polytechnique

Exposé par Kaveh Mousavand: «Brauer-Thrall Conjectures, Old and New!»

Speaker: Kaveh Mousavand
Location: Salle Flajolet, LIX
Date: Wed, 13 Nov 2019, 10:30-11:30

Ce mercredi à 10h30 nous aurons le plaisir d'écouter Kaveh Mousavand (UQAM) nous parler de «Brauer-Thrall Conjectures, Old and New!».

Le programme du séminaire est disponible ici : https://galac.lri.fr/pages/combi-seminar.html

À mercredi, Jérémie, Éric et Viviane.

Résumé: τ-tilting theory is an elegant -- but technical -- subject in representation theory of associative algebras, with motivations from cluster algebras. It was introduced by Adachi-Iyama-Reiten, in 2014. However, thanks to the recent result of Demonet-Iyama-Jasso, one can fully phrase the concept of τ-tilting finiteness in terms of linear algebra. I adopt this elementary approach to share some new results on τ-tilting finiteness of several families of algebras with rich combinatorics.

I begin with a review of two fundamental conjectures by Brauer and Thrall. After some historical remarks on those, I present a gentle introduction to τ-tilting finiteness, which allows me to state a conjecture of similar nature that relies on my recent work on τ-tilting theory. I will share my main strategy, as well as my new results on some cases.

I will not assume any prior knowledge of representation theory of algebras!