We organise an informal seminar on infinite dimensional quantum symmetric pairs and quantum gravity where we study and discuss various topics in this area with staff, postdocs and PhD-students. 

The informal RU-UvA seminar is organised by Jort de Groot (UvA) and Stein Meereboer (RU). Please send an email to Stein Meereboer (stein.meereboer "_--at--_"ru.nl) if you want to be on the email list for further announcements.

Time schedule (2025-2026)


2026, spring session


Jort de Groot (UVA)

Title: Quantum gravity, holography and the DSSYK model

Abstract: In this talk I will explain the basics of the problem of quantum gravity, and how this leads to the idea of holography. Then, I will shift focus to a specific holographic model, the SYK model, and its double scaled limit (the DSSYK model). For this model, I will explain how there is an underlying quantum group symmetry, and why the correct point of view for this quantum group symmetry is the locally compact setting.

Timothy Budd (Radboud)

Title: Schwarzian Field Theory via Random Geometry

Abstract: Rigorous probabilistic constructions of interacting (Euclidean) QFTs are few and far between. Two recent additions to this list, Liouville Conformal Field Theory (LCFT) and Schwarzian Field Theory (SFT), both arising in a quantum gravity context, have natural interpretations in random geometry. In this context, I will explain how SFT is obtained rigorously as a limit of random hyperbolic polygons. Depending on time I will comment on the relation between the probabilistic and group-theoretic perspectives on the model, or on how LCFT analogously should arise as a limit of random hyperbolic polyhedra. Based on w.i.p. with Leonid Chekhov and recent work with Nicolas Curien. 

Max van Horssen (KU Leuven)

Title: Shift operators and their non-symmetric analogs in Heckman-Opdam and Macdonald theory

Abstract: In this talk, we give an introduction to shift operators for the (non-)symmetric Heckman-Opdam polynomials and the (non-)symmetric Macdonald-Koornwinder polynomials. We begin by recalling algebraic properties of symmetric shift operators, including their structure theorem and Heckman’s construction. We then explain how these shift operators were used by Opdam in his resolution of the Macdonald constant term conjectures at q = 1.

More recently, Opdam and Toledano Laredo announced the existence of a non-symmetric analog of the symmetric shift operators in the Heckman-Opdam setting, relying on transcendental methods. In rank one, explicit non-symmetric shift operators were obtained in joint work with van Pruijssen (Jacobi setting) and Schlösser (Askey-Wilson setting) using techniques involving matrix-valued orthogonal polynomials. We outline this approach and explain its relation to polynomial solutions of the KZ-equations.

Already in 1994, Felder and Veselov constructed a shift operator for the KZ-equations for fixed spectral parameters. Inspired by their approach, we present an algebraic construction that associates a forward and backward non-symmetric shift operator to each linear character of the Weyl group. With minor adjustments, this construction also yields the existence of similar non-symmetric shift operators in the Macdonald-Koornwinder setting.

This talk is based on joint work with Maarten van Pruijssen (arXiv:2602.06784).



Stein Meereboer

Title: An introduction to quantum affine symmetric pairs

Abstract: Classical symmetric pairs consist of a Kac-Moody algebra together with a subalgebra of fixed points under an involutive automorphism. Quantum symmetric pairs, as introduced by Letzter and Kolb, provide a quantization of this pair of algebras in the form of a Drinfel'd-Jimbo quantum group and a coideal subalgebra specializing to the classical universal enveloping algebras. Infinite dimensional symmetric spaces quantize the corresponding algebras of invariant functions. In this talk we will gently introduce these concepts and will serve as preparation for Philip's talk. We will mainly consider affine sl 2, its diagonal symmetric pair, and the q-Onsager algebra.