## Time and location

The Ottawa-Carleton joint algebra seminar meets during the academic year approximately once per week at either The University of Ottawa or Carleton University. Unless otherwise indicated, time and location are as follows:

• University of Ottawa:  Thursday, 2:30pm–3:30pm, STM 664
• Carleton University:  Thursday, 2:30pm–3:30pm, HP 4325

## Talks

Date Speaker Title (click for abstract)
Sep 12 (O) Alistair Savage (Ottawa)
Deligne’s category Rep$$(S_t)$$ is a linear monoidal category that interpolates between the representation theory of the symmetric groups. In particular, it is defined even when $$t$$ is not a natural number. However, $$t$$ is fixed. On the other hand, the Heisenberg category encapsulates the representation theory of all the symmetric groups $$S_n$$ (for all natural numbers $$n$$) and the canonical induction and restriction functors between their module categories. It categorifies the Heisenberg algebra and has some deep connections to Hilbert schemes and quiver varieties. In this talk we will describe an embedding of Deligne’s category into the Heisenberg category. We will discuss some nice properties of this embedding and mention how it leads to some natural further directions for research. This is joint work with Samuel Nyobe Likeng and Christopher Ryba.
Sep 19 (O) Hadi Salmasian (Ottawa)
Given a multiplicity-free action $$V$$ of a simple Lie (super)algebra $$\mathfrak{g}$$, one can define a distinguished basis for the algebra of $$\mathfrak{g}$$-invariant differential operators on $$V$$. The problem of computing the eigenvalues of this basis was first proposed by B. Kostant, and is closely related to the theory of interpolation Jack polynomials and their generalizations. In this talk, we concentrate on an example of similar spirit, associated to the orthosymplectic Lie superalgebras, and compute two formulas for the eigenvalues of the corresponding Capelli operators. Along the way, the Dougall-Ramanujan identity appears in an unexpected fashion. This talk is based on a joint work with Siddhartha Sahi and Vera Serganova.
Sep 26
Oct 3
Oct 10
Oct 17 (C) Eleonore Faber (Leeds)
TBA
Oct 24
Oct 31 (O) Philippe Gille (Lyon)
Can one hear have the shape of a drum? In other words, to which extent is a Riemannian manifold determined by the spectrum of its Laplace operator? Prasad and Rapinchuk investigated the case of locally symmetric spaces which relates to subtori of algebraic groups and then with non-abelian Galois cohomology. We shall survey results on this algebraic theme by the preceding authors, Beli-G.-Lee, Chernousov-Rapinchuk-Rapinchuk and others.
Nov 7
Nov 14
Nov 21
Nov 28
Dec 5
(O) = uOttawa, (C) = Carleton