PIMS Geometry, Algebra and Physics Seminar

Organized by Alex Weekes, Steve Rayan and Curtis Wendlandt


Schedule (2022-2023)

Talks are normally held on Thursdays at 4:00-5:30pm CST, and each can 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. 



Title and Abstract

Thursday, October 13th



Maggie Miller

Obstructing isotopy with an extra dimension

In 1982, Livingston showed that several examples of Seifert surfaces that are not isotopic in the 3-sphere become isotopic when pushed into the 4-ball. This is consistent with a common intuition in topology: objects that are somehow similar should become the same when stabilized. We recently constructed families exhibiting that this is not always the case — that is, surfaces in the 3-sphere that remain non-isotopic even when pushed into the 4-ball. This is joint work with Kyle Hayden, Seungwon Kim, JungHwan Park, and Isaac Sundberg.

Thursday, November 24th



Michael Groechenig

Complex K-theory of dual Hitchin systems

I will report on joint work with Shiyu Shen. Moduli spaces of \(\mathrm{SL}(n)\) and \(\mathrm{PGL}(n)\)-Higgs bundles are conjecturally related by a derived equivalence and (up to HK rotation) mirror symmetry. This talk will be devoted to a shadow of these equivalences in complex K-theory.

Thursday, December 15th

4:30-6:00pm CST



Aleksei Ilin 

Bethe subalgebras of Yangians

The main object of this talk is the family of commutative Bethe subaglebras in the Yangian. It is a natural family of commutative subalgebras of the Yangian parameterized by the simple adjoint Lie group. In my talk I will discuss how this family is connected with various wonderful compactifications. I also plan to discuss applications of this family to the theory of crystals.


Thursday, February 2nd

4:30-6:00pm CST


Matthew B. Young

\(U_q(\mathfrak{gl}(1 \vert 1))\) and \(U(1 \vert 1)\) Chern-Simons theory

Chern-Simons theory, as introduced by Witten, is a three dimensional quantum gauge theory associated to a compact simple Lie group and a level. The mathematical model of this theory as a topological quantum field theory was introduced by Reshetikhin and Turaev and is at the core of modern quantum topology. The goal of this talk is to explain a non-semisimple modification of the construction of Reshetikhin and Turaev which realizes Chern-Simons theory with gauge supergroup \(U(1 \vert 1)\), as studied in the physics literature by Rozansky-Saleur and Mikhaylov. In particular, I'll motivate and explain various relative modular structures on the category of representations of the quantum group of \(\mathfrak{gl}(1 \vert 1)\) which should be seen as non-semisimple analogues of modular tensor categories associated to the quantum representation theory of a simple Lie algebra at a root of unity. Based on joint work with Nathan Geer.

Wednesday, May 3rd

4-5:30pm CST


Gabe Islambouli

Multisections and Bridge multisections

In 2016, Gay and Kirby showed that every compact smooth 4-manifold can be decomposed into three standard pieces. A particularly nice feature of this decomposition is that the smooth topology of the 4-manifold can be encoded by curves on a surface. In this talk, we explore the consequences of allowing more pieces in this decomposition, and show that many interesting cut and paste procedures can be carried out by natural mapping classes on the surface. We also explore a related decomposition for knotted surfaces in a 4-manifold.

Friday, May 12th



Puttipong Pongtanapaisan

Random knotting and linking

Back in the old days, before the invention of Apple Wireless Airpods, people were more familiar with the tendency of the headphones in their pockets to become knotted. It seems natural to expect that the probability that a random curve is tangled increases with its length. In fact, Frisch, Wasserman, and Delbrück conjectured that sufficiently long ring polymers will be knotted with high probability. In this talk, I will discuss some models where the conjecture is known to be true, including a setting that I investigated with Jeremy Eng, Chris Soteros, and Rob Scharein. Topological techniques used in the proofs such as finite-type invariants will also be discussed.

Thursday, August 3rd 



Sachin Gautam

 R-matrices of affine Yangians

Yangians are certain remarkable Hopf algebras, associated to finite-dimensional simple Lie algebras, introduced by Drinfeld in the 1980's. Drinfeld proved, in a non-constructive manner, that each Yangian comes equipped with a formal solution to the famous Yang-Baxter equation, known as Drinfeld's universal R-matrix.
In this talk, I will present a very concrete method to construct Drinfeld's universal R-matrix using additive difference equations. I will explain how our method generalizes to other situations where no analogue of Drinfeld's result is known, such as Yangians associated to affine Kac-Moody algebras. I will highlight the significant differences between the finite and affine situations, and the new challenges present in the latter.
This talk is based on earlier works joint with Valerio Toledano Laredo and Curtis Wendlandt, and a recent one in collaboration with Andrea Appel and Curtis Wendlandt.