AGQ integrability seminar
This is an informal gathering of people interested in integrable systems from the University of Edinburgh, Heriot-Watt University and the University of Glasgow.
The seminar runs bi-weekly on Thursdays alternating between Edinburgh (Bayes Centre, room 5.46) and Glasgow (University of Glasgow, School of Mathematics and Statistics, usually room 311B).
Organizers: Sasha Shapiro (UoE), Yegor Zenkevich (UoE), Robert Weston (HWU), Alexander Cooper (HWU), Anton Izosimov (UoG), Jules Lamers (UoG), Christian Korff (UoG).
Next seminars:
January 22, 2025, Edinburgh, venue TBA, speaker TBA
February 4, 2026, Glasgow, venue TBA
13:00 Bart Vlaar (BIMSA)
On quantum groups, old and new
Quantum groups (= quantized universal enveloping algebras) were defined by Drinfeld and by Jimbo in the mid 1980s, generalizing a construction by Kulish and Reshetikhin. In addition to their origin in mathematical physics, they are objects of interest in (non-commutative) geometry, (harmonic and functional) analysis and (low-dimensional) topology, as well as pure representation theory. We will discuss a more recent, more general, but related family of algebras called quantum symmetric pairs or i-quantum groups, with a focus on the topological viewpoint and the application to quantum integrable systems. We will discuss some recent progress and some open problems. Mainly based on joint works with Andrea Appel, and with Alec Cooper and Robert Weston.
Past seminars:
December 4, 2025, Edinburgh (UNUSUAL LOCATION: G.02, 19 George Square)
13:00 Sasha Shapiro (University of Edinburgh)
Integrable systems, character varieties, and clusters
Phase spaces of many famous integrable systems, such as Toda, Ruijsenaars, Gelfand-Tsetlin, etc, can be realised as character varieties. In turn, cluster structure on the latter allows for combinatorial description of these integrable systems, and is helful in the study of their discrete dynamics and Hamiltonian eigenfunctions. During the talk I will discuss some of these topics focusing on low-dimensional examples.
November 6, 2025, Edinburgh (UNUSUAL LOCATION: room LT1, Appleton Tower)
13:00-13:45 Alec Cooper (Heriot-Watt University)
Preseminar: A Brief Discussion of Quantum Groups and Diagrams
14:15-15:45 Robert Weston (Heriot-Watt University)
The algebraic description of open quantum spin chains
October 23, 2025, Glasgow (UNUSUAL LOCATION: room 513, Boyd Orr building)
Misha Feigin (University of Glasgow)
Cherednik algebras and Calogero-Moser type systems
This is going to be an introductory/overview talk. I’m going to define rational Cherednik algebras, discuss their basic properties and representations, some important subalgebras, and related integrable systems.
October 9, 2025, Edinburgh (UNUSUAL LOCATION: Lecture Theatre A, 40 George Square)
13:00-13:45 Mikhail Vasiliev (University of Glasgow)
Introduction to cluster algebras
I will give a brief introduction to cluster algebras. We will discuss several simple examples to illustrate how the machinery of cluster algebras work. I will also introduce Poisson structure arising in cluster algebras, which will be used by Anton in his talk.
14:15-15:45 Anton Izosimov (University of Glasgow)
Cluster integrable systems
We’ll start with discussing the notion of a cluster integrable system due to Goncharov and Kenyon, along with a few examples of such systems. Then I’ll explain why such systems can be viewed as “type A” objects and discuss how to construct their counterparts for (some) other Dynkin types.
September 25, 2025, Glasgow
Yegor Zenkevich (University of Edinburgh)
Introduction to quantum toroidal algebras and integrability
Seminar notes:
