Current

Ongoing seminar series

Autumn Session

Kenny De Commer (Vrije Universiteit Brussel) - November 3, 2025

• Title: Braided tensor product of von Neumann algebras

• Abstract: Work of Meyer, Roy and Woronowicz has shown that the category of C*-algebras with an action by a quasi-triangular quantum group admits a monoidal structure by means of a braided tensor product. We have shown that a similar result holds if instead we work with actions on von Neumann algebras. Moreover, particular to this setting, we are able to show how (part of the) modular theory of a braided tensor product behaves. We will frame the latter result in a more general setting of cocycle deformations. This is joint work with J. Krajczok.

• Slides

Joeri De Ro (IMPAN) - November 10, 2025

• Title: Equivariant Eilenberg-Watts theorems for locally compact quantum groups

• Abstract: Given actions of a locally compact quantum group \(G\) on the von Neumann algebras \(A\) and \(B\), we can associate to it the category \(\operatorname{Corr}^G(A,B)\) of G-A-B-correspondences. Special cases of this category include the category \(\operatorname{Rep}(A)\) of unital, normal \(*\)-representations of \(A\) on Hilbert spaces and the category \(\operatorname{Rep}^G(A)\) of unital, normal, \(G\)-representations on Hilbert spaces. We construct actions \(\operatorname{Rep}^G(A)\curvearrowleft \operatorname{Rep}(G)\) and \(\operatorname{Rep}(A)\curvearrowleft \operatorname{Rep}(\hat{G})\), providing us with natural examples of module categories. We show that the categories of module functors \(\operatorname{Rep}(B)\to \operatorname{Rep}(A)\) and \(\operatorname{Rep}^G(B)\to \operatorname{Rep}^G(A)\) are both equivalent to the category of \(G\)-\(A\)-\(B\)-correspondences, providing equivariant versions of the von Neumann algebraic Eilenberg-Watts theorem.

• Slides

Milan Donvil (École normale supérieure - PSL) - November 17, 2025

• Title: W\(^*\)-superrigidity for discrete quantum groups

• Abstract: A (countable) group is called W*-superrigid if it is completely remembered by its group von Neumann algebra in the following sense: if another group gives rise to an isomorphic group von Neumann algebra, the groups must be isomorphic. In the past fifteen years, several classes of W*-superrigid groups have been found. However, it turns out that many of these groups are not W*-superrigid in the larger class of compact quantum groups: their group von Neumann algebras admit different quantum group structures. In a recent work with Stefaan Vaes, we found the first examples of compact quantum groups which are ‘quantum W*-superrigid’. To obtain quantum W*-superrigidity, we had to combine three different types of results: vanishing of cohomology, rigidity of (quantum) groups relative to a family of (quantum) group automorphisms, and deformation/rigidity theory. I will explain why each of these three parts is essential and how they come together to prove our main result.

• Slides

Leandro Vendramin (Vrije Universiteit Brussel) - November 24, 2025

• Title: Nichols algebras over (solvable) groups

• Abstract: Nichols algebras appear in various areas of mathematics, ranging from Hopf algebras and quantum groups to Schubert calculus and conformal field theory. In this talk, I will review the main challenges in classifying Nichols algebras over groups and discuss some recent classification theorems. In particular, I will highlight a recent classification result (https://arxiv.org/abs/2411.02304), achieved in collaboration with Andruskiewitsch and Heckenberger, concerning finite-dimensional Nichols algebras over solvable groups.

• Slides

David Jaklitsch (University of Oslo) - December 16, 2025

• Title: The braided monoidal structure of tube algebra representations

• Abstract: Ocneanu’s tube algebra plays a central role in lattice models of Levin-Wen type, where topological excitations are given by irreducible representations. The purpose of the talk is to report on our recent results explicitly describing the tensor product of tube algebra representations and the braiding. The well-known linear equivalence between tube algebra representations and the Drinfeld center category is (by means of this structure) upgraded to a braided monoidal equivalence. This is joint work with Makoto Yamashita.

• Slides

Winter Session

Jennifer Brown (University of Edinburgh) - January 19, 2026

• Title: Parabolic Reduction and Quantum Character Varieties

• Abstract: Character varieties parametrise G-local systems on topological spaces, for G a reductive group. They play a central role in physical models such as Chern-Simons theory and have been widely studied. Many constructions involving character varieties can be formulated with a combination of skein theory and parabolic reduction along a Borel subgroup of G. We’ll tell this story, with the guiding goal of defining quantum cluster coordinates on quantised character varieties. This is based on joint work with David Jordan.

Bin Gui (Tsinghua University) - TBA, 2026

• Title: TBA

• Abstract: TBA