Algebra Seminar

Winter 2026 (Fridays 3:00-4:00, STEM664)

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January 26 (13:00, STEM 664)

Ekta Tiwari (UOttawa)

Seeing representations of a group through the lens of its maximal compact subgroups

Abstract: A classical problem in representation theory is to understand how an irreducible representation of a group decomposes when restricted to its subgroups. Such questions are commonly referred to as branching problems.

In this talk, we will explore the restriction of irreducible smooth representations of the unramified quasi-split unitary group U(1,1) to its hyperspecial maximal compact subgroup K. We will present explicit branching rules in this setting and discuss several applications that arise from having a concrete description of these restrictions.

(This talk assumes familiarity with basic notions in representation theory.)

February 27 (15:00, STEM 664)

Rui Xiong (UOttawa)

Bumpless Pipe Dreams meets Clans

Abstract: Let (G,K) be a symmetric pair. The subgroup K is spherical, meaning there are finitely many K-orbits on the flag variety G/B. In this talk, I will explain the general theory of symmetric pairs from this perspective. We will then focus on the case (G,K)=(GLn, GLp x GLq) (n=p+q), where the K-orbits are indexed by combinatorial objects called (p,q)-clans. I will explain how bumpless pipe dreams relate to the equivariant geometry of these orbit closures. This is joint work with Yiming Chen, Neil Fan, and Ming Yao.

March 6 (15:00, STEM 664)

Sean Cotner (University of Michigan, Ann Arbor)

Propagating congruences in the local Langlands program

Abstract: We will recall some features of the local Langlands program, as well as several concrete proposals for the local Langlands correspondence. After this, we will discuss partial calculations of the Fargues–Scholze L-parameters associated to tame supercuspidal representations of reductive p-adic groups, by chaining together some instances of “modular functoriality”. This is joint work with Tony Feng.

March 13 (15:00, STEM 664)

Yaolong Shen (UOttawa)

Module subcategories arising from symmetric pairs

Abstract: Classical symmetric pairs $(\mathfrak g,\mathfrak k)$ play an important role in Lie theory and representation theory, and their quantum analogues—quantum symmetric pairs—have motivated various diagrammatic categories. As a consequence of the coideal structure, many of these categories carry a natural action of a tensor category.

In this talk, we discuss how to classify submodules of a category $\mathcal M$ equipped with an action of a tensor category $\mathcal C$. When $\mathcal M=\mathcal C$, this reduces to the classification of tensor ideals. As an example, we illustrate the result using the disoriented skein category, which underpins tensor modules for certain quantum symmetric pairs.

This is joint work with Hadi Salmasian and Alistair Savage.