¾ÅÐãÖ±²¥

Math & Stats Department Colloquium

Friday, October 29th, 2021

Time: 2:30 p.m.  Place: Online (via Zoom)

Speaker: Kaveh Mousavand (¾ÅÐãÖ±²¥)

Title: An elementary approach to an open conjecture in $\tau$-tilting theory

Abstract: In 2014, Adachi-Iyama-Jasso introduced the concept of $\tau$-tilting theory in the setting of finite dimensional algebras. This modern approach to the notion of mutation of tilting modules soon received a lot of attention and established fruitful connections to other areas, including homological algebras, cluster algebras, lattice theory, etc. Motivated by the algebro-geometric aspects of representation theory, in 2019 I proposed a conjectural equivalence for $\tau$-tilting finiteness of algebras in terms of irreducible components of module varieties. The conjecture has proved to be novel and can result in new linkages between the aforementioned domains. In this talk, I adopt an elementary approach to the study of this open conjecture and present it as a problem in linear algebra. Namely, I fully avoid the technicality of the subject and only use linear algebra and assume familiarity with rudiments of module theory. I begin with some background to motivate the conjecture, then outline our general methodology in the treatment of the problem, and end with some new results from my recent joint work with Charles Paquette, where we verify the conjecture for some important cases.

Kaveh Mousavand is a Coleman postdoctoral fellow in the Department of Mathematics and Statistics at ¾ÅÐãÖ±²¥. He obtained his Ph.D.~from Universite du Quebec Montreal in 2020. His research interests include representation theory of algebras, $\tau$-tilting theory, cluster algebras, and algebraic combinatorics.