Réunion d'hiver SMC 2026
Montréal, 11 - 14 décembre 2026
Théorie des représentations
Org: Alistair Savage (University of Ottawa) et Alex Weekes (Université de Sherbrooke)
[PDF]
Org: Alistair Savage (University of Ottawa) et Alex Weekes (Université de Sherbrooke)
[PDF]
- JON BORETSKY, McGill
- EMILY CLIFF, Université de Sherbrooke
- PATTY COMMINS, UQAM
- IVAN DIMITROV, Queen's University
- MONICA GARCIA, UQAM
- NICOLLE GONZÁLEZ, University of British Columbia
- NIKITA GRYGORYEV, Perimeter Institute
- JOEL KAMNITZER, McGill
Skein algebras of punctured spheres, Coulomb branches and knot homology [PDF]
- EMILY CLIFF, Université de Sherbrooke
-
Certain skein algebras of surfaces are expectied to be isomorphic to K-theoretic Coulomb branch algebras. This suggests that these algebras can be categorified using coherent sheaves on BFN spaces. I will explain how we can combine my older work with Cautis into this perspective in order to obtain homological knot invariants for knots in thickened punctured spheres.
- NICCOLO MATTAREI, University of Ottawa
- THOMAS MORAN, University of Ottawa
- MONICA NEVINS, University of Ottawa
Representations of p-adic groups near the identity [PDF]
- THOMAS MORAN, University of Ottawa
-
The infinite-dimensional irreducible representations of p-adic groups have an elegant geometric structure near the identity. The analytic nature of this structure, expressed in terms of the character of the representation, has been known since the 1970s, and recently progress has been made on understanding it in more concrete terms via the restriction of representations to sufficiently small compact open subgroups. In this talk, we describe the ideas and the techniques involved, focusing on geometric and combinatorial aspects. Parts of this talk are based on ongoing joint work with Ekta Tiwari (IISER Pune), with Zander Karaganis (UBC), and with David Schwein (Utah).
- THEO PINET, McGill
- ANDREW RIESEN, M.I.T.
- HOMA ROUDINI, University of Ottawa
- LEONID RYBNIKOV, Université de Montréal
- HADI SALMASIAN, University of Ottawa
- JAKE S. ZIMMERMANN SIMMONS, University of Toronto
Regular Bisections of Nilpotent Subalgebras of $\mathfrak{sl}(n)$ [PDF]
- ANDREW RIESEN, M.I.T.
-
In this talk, we explore how nilpotent regular
Lie subalgebras $\mathfrak{g}$ of the special linear algebra $\mathfrak{sl}(n)$ can be
split into bisections, pairs of subalgebras of $\mathfrak{g}$ that
equal $\mathfrak{g}$ as a vector space
direct sum.
These splittings help reveal internal structure of the
$\mathfrak{g}$ and provide a concrete way to understand how its
parts fit together, through a matrix representation
of the bisections. There is a classical
bijection between biclosed subsets of root systems and
biclosed subsets of root systems.
In this talk we
will investigate a counting of bisections of the
strict upper triangle algebra $\mathfrak{n}(n) \subseteq \mathfrak{sl}(n)$
which provides a new perspective on this bijection,
and will discuss how this could lead to
investigations using the Weyl group of a matrix
representations of bijections, implicitly giving
a group structure on all bisections any nilpotent
regular subalgebra of $\mathfrak{sl}(n)$. There will be $n!$
bisections of $\mathfrak{n}(n)$ and this will be proven.
The proof uses an induction argument that
introduces the idea of extending algebras, and those
extensions being complementary to each other.
Only the bisections of some algebras can be
represented as matrices, but all are relevant to the Weyl
group as structure of bisections in general can
be inherited by those that can be represented as matrices.
Lastly,
we present an algorithm, which we will call the falling
terms algorithm, to count bisections of subalgebras of the
strict upper triangle.
- JOSHUA SUSSAN, CUNY Medgar Evans College
- ALEKSANDR (SASHA) TRUFANOV, University of Montreal
- BEN WEBSTER, University of Waterloo
- MERI ZAIMI, Perimeter Institute for Theoretical Physics
- KIRILL ZAYNULLIN, University of Ottawa
- ALEKSANDR (SASHA) TRUFANOV, University of Montreal