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).


Jasper Stokman

Title: Hecke algebraic deformations of discrete quantum walks.

Abstract: I will explain that there is a fruitful interplay between representation theory of the infinite dihedral group and the theory of discrete quantum walks. I will then introduce 2-parameter deformations of discrete quantum walks using the observation, going back to H. Matsumoto (1977), that the rank one affine Hecke algebra is isomorphic to the group algebra of the infinite dihedral group.  If time permits, I will give criteria for the existence of perfect state transfer in these deformed discrete quantum walks.

Mikhail Isachenkov

Title: Von Neumann algebraic quantum group symmetry of the DSSYK model

Abstract: I will pick up at the point where Jort stopped last time. My goal will be to explain the role played by a specific von Neumann algebraic (vNa) quantum group SU_q(1,1)⋊Z_2 in description of the double-scaled SYK model (DSSYK), which is an important toy model capturing various features we expect from more realistic models of quantum gravity. To get there, I will first review Liouville quantum mechanics (and its usual interpretation as a toy quantum gravity model), and show how the normaliser of the classical Lie group SU(1,1) inside its complexification appears as a dynamical symmetry of this system. Then I will recall the construction of the von Neumann algebraic quantum group providing the appropriate quantum group deformation of that normaliser, and explain the brand new (generalised) Gauss decomposition of this quantum group. I will then show how spectral analysis of the Casimir of SU_q(1,1)⋊Z_2 (adapted to the specific instance of the Gauss decomposition) describes the DSSYK dynamics. Time permitting, I might go into more detail regarding the consequences of the vNa quantum group structure that we uncovered for the bulk quantum gravity observables, such as the discreteness of the spectrum of an observable corresponding to geodesic length in the bulk. This talk is based on the paper 2512.10101 with Koen Schouten.

Stein Meereboer

Title: An overview of quantum symmetric pairs in terms of generalized Satake diagrams 

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 I will give an overview of these concepts in the setting of Lusztigs quantized enveloping algebras and the recently introduced generalized Satake diagrams of Vlaar and Regelskis. If time permits we will study their associated (infinite dimensional) quantum symmetric spaces.