# Brauer-Thrall Conjectures, Old and New!

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Time: 10:30 -- Location: Salle Philippe Flajolet du LIX

$$\tau$$-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 $$\tau$$-tilting finiteness in terms of linear algebra. I adopt this elementary approach to share some new results on $$\tau$$-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 $$\tau$$-tilting finiteness, which allows me to state a conjecture of similar nature that relies on my recent work on $$\tau$$-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!

Category: seminars
Tags: Combi seminar combinatorics