Algebra Seminar

Winter 2025

Fridays, 2:30-3:30pm

UOttawa (STEM 664) / Carleton (HP4325)

January 24 (Carleton)

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Speaker: Kaveh Mousavand (Okinawa Institute of Science and Technology)

Title: Hom-orthogonal modules and geometry of representation varieties

Abstract: Originally motivated by some open conjectures in representation theory of finite dimensional algebras, we study the sets of pairwise Hom-orthogonal modules. In particular, we relate the study of arbitrary Hom-orthogonal modules to the distribution of bricks (a.k.a Schur representation) and consequently prove some new results on the geometry of representation varieties. For an algebra A, we use some algebraic and geometric tools to find necessary and sufficient conditions for the existence of an infinite family of Hom-orthogonal A-modules of the same dimension. This is based on joint work with Charles Paquette.

February 7 (UOttawa)

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Speaker: Erhard Neher (Ottawa)

Title: Azumaya algebras with orthogonal involutions

Abstract: Azumaya algebras are the commutative ring version of central simple algebras over fields, for example matrix algebras. Orthogonal involutions are the analogue of the transpose involution of matrix algebras. For applications in the theory of algebraic groups, it is important to investigate so-called semi-traces associated with Azumaya algebras with orthogonal involutions. In this talk, I will describe their theory over rings, and if time sketch what is known over schemes. The talk is based on joint work with Philippe Gille and Cameron Ruether.