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SUMMARY:Kaveh Mousavand (OIST)
DTSTART:20231212T073000Z
DTEND:20231212T083000Z
DTSTAMP:20260423T035821Z
UID:OISTRTS/53
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OISTRTS/53/"
 >Some applications of bricks in classical and modern problems in represent
 ation theory</a>\nby Kaveh Mousavand (OIST) as part of OIST representation
  theory seminar\n\n\nAbstract\nBricks (also known as Schur representations
 ) form a special subfamily of indecomposable modules\, and they are used i
 n the algebraic and geometric study of representation theory of algebras. 
 We start by looking at some classical results on bricks\, including a char
 acterization of locally representation-directed algebras (due to Dräxler)
 . Then\, we consider some new directions of research in which bricks have 
 played crucial roles. More specifically\, we briefly recall an elegant cor
 respondence between bricks and indecomposable $\\tau$-rigid-modules (due t
 o Demonet-Iyama-Jasso)\, which has many applications in $\\tau$-tilting th
 eory. We use the notion of $\\tau$-rigidity to give a new characterization
  of locally representation-directed algebras\, and to further generalize t
 his family. If time permits\, we also report on some new results on an ope
 n conjecture (so-called the 2nd brick-Brauer-Thrall conjecture) which I po
 sed in 2019. Part of this talk is based on my recent joint work with Charl
 es Paquette.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/53/
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