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.
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.
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.
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.
TBA - December 15, 2025
Title: TBA
Abstract: TBA