Quantum groups and quantum probability

Procope/DAAD project, January 2019 - December 2020

Funded by Procope and DAAD.

Coordinators: Roland Vergnioux (Caen, France) and Moritz Weber (Saarbrücken, Germany).


For the travel reimbursement of participants from the German side, fill in the reimbursement form in German or in English, sign it (!) and send it together with your travel tickets and hotel bills to Moritz Weber.
The travel reimbursement is by fixed per diems plus a fixed travel sum, see Pauschalen.

Scientific goals

We intend to study compact quantum groups and their interplay with quantum probability and free probability under operator algebraic and algebraic, quantum probabilistic and probabilistic, as well as purely combinatorial aspects. Our focus is on the (free) quantum versions O_N+ and S_N+ of the orthogonal resp. the symmetric group. They are part of the class of so called easy quantum groups, a class which received a lot of attention in the past ten years. Easy quantum groups are compact quantum groups with a highly combinatorial representation theory.

One main aspect of our project is to push forward our understanding of O_N+ and S_N+ and to extend the insight to the whole class of easy quantum groups. This is part of the big program to understand all compact quantum groups of matrix type. We believe that quantum probabilistic tools such as Lévy processes and other stochastic processes are a key to answering our questions. Amongst others, they are linked to cohomological considerations as well as to the representation theory of quantum groups.

We identify the following six work packages.
  • (1) Representation Theoretical Properties of Easy Quantum Groups
  • (2) Free Entropy Dimension and Connes's Embedding Problem
  • (3) Cohomology and L^2-Betti Numbers
  • (4) K-theory
  • (5) Quantum Lévy Processes
  • (6) Quantum Probabilistic Boundaries

Participants from France

Participants from Germany

Updated: 27 March 2019   Moritz Weber Impressum