PIMS Geometry, Algebra and Physics Seminar
Organized by Alex Weekes, Steve Rayan and Curtis Wendlandt
Schedule (2024-2025)
Talks are normally held on Thursdays at 4:00-5:30pm CST, and can usually be attended virtually via Zoom (including those talks held in-person at the University of Saskatchewan) using the following information:
| Meeting ID | Passcode | Link |
|---|---|---|
| 936 6357 4827 | qUSaskGAP | Here |
The seminar is intended to be informal and accessible to graduate students studying algebra, geometry, or mathematical physics. Speakers typically prepare an hour-long talk, with the remaining half hour dedicated to discussion and questions.
Date/Location |
Speaker |
Title and Abstract |
|---|---|---|
|
April 22nd 4-7:30PM CST (In-person only) THORV 124 |
Eric Boulter, Davood Nejaty, Raphaël Belliard |
GAP Mini-SymposiumSpeaker 1: Eric Boulter (University of Saskatchewan) — 4:00-5:00PM Title: Spectral covers without embeddings Abstract: Higgs bundles and their twisted variations feature a spectral correspondence relating a V-twisted Higgs bundle on X with the spectral data of a finite cover C ⊆ Tot(V) of X and a torsion-free sheaf on C. In this talk we will look at twisted Higgs bundles in a general setup, and compare the traditional spectral correspondence to a generalized version where we associate a Higgs bundle to a torsion-free sheaf on a finite cover C of X without assuming that C embeds into the total space of the twisting bundle V. We will also do some more explicit computations in the case of an Abelian cover. Speaker 2: Davood Nejaty (University of Melbourne) — 5:15-6:15PM A topological mirror symmetry for pairs of commuting Higgs fields For a smooth projective complex curve C, a reductive group G, and a pair of line bundles L1 and L2 on C such that L1⊗L2 is isomorphic to KC, we introduce a moduli space of stable commuting Higgs bundles. Inspired by the Hausel-Thaddeus conjecture for Higgs bundles, we conjecture the equality of the E−polynomials for the moduli spaces of stable SLn and PGLn commuting Higgs bundles. The conjecture uses an equivariant localization. We prove the conjecture for n = 2 and even degree line bundles L1 and L2. Speaker 3: Raphaël Belliard (University of Saskatchewan) — 6:30-7:30PM The quantum geometry of complex curves emerging from enumeration problems
The method of the generating function is one of the most powerful tools to approach enumeration problems from a complex analysis viewpoint. Gathering numbers of interest in a series can indeed often transform the underlying recursive structures into functional relations. When these functional relations can be interpreted in terms of representation theory of conformal algebras, the relevant data can be encoded in the geometry of a meromorphic local system on a Riemann surface: the quantum curve of the problem. After considering the examples of the generalised Catalan numbers and r-spin intersection numbers, we will describe their quantum curves and what generally makes them deserve that name.
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