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).

Reimbursement

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

Isabelle Baraquin, Université de Franche-Comté, Besancon
Julien Bichon, Université Clermont Auvergne, Clermont-Ferrand
Léonard Cadilhac, Université de Caen Normandie, Caen
Pierre Fima, Paris 7
Uwe Franz, Université de Franche-Comté, Besancon
Amaury Freslon, Université Paris-Sud XI, Orsay
Yulia Kuznetsova, Université de Franche-Comté, Besancon
Christian Le Merdy, Université de Franche-Comté, Besancon
Rubén Martos, Paris 7
Éric Ricard, Université de Caen Normandie, Caen
Frank Taipe, Université de Caen Normandie, Caen
Pierre Tarrago, Sorbonne Université, Paris
Roland Vergnioux, Université de Caen Normandie, Caen
Hua Wang, Paris 7
Simeng Wang, Université Paris-Sud XI, Orsay
Xumin Wang, Université de Franche-Comté, Besancon
Jared White, Université de Franche-Comté, Besancon
Xu Quanhua, Université de Franche-Comté, Besancon
Haonan Zhang, Université de Franche-Comté, Besancon

Participants from Germany

Vadim Alekseev, TU Dresden
Marwa Banna, Saarland University, Saarbrücken
Malte Gerhold, University of Greifswald
Daniel Gromada, Saarland University, Saarbrücken
Stefan Jung, Saarland University, Saarbrücken
Ulrich Krähmer, TU Dresden
Felix Leid, Saarland University, Saarbrücken
Myriam Mahaman, TU Dresden
Manuel Martins, TU Dresden
Miguel Angel Pluma Rodriguez, Saarland University, Saarbrücken
Lucia Rotheray, TU Dresden
Simon Schmidt, Saarland University, Saarbrücken
Roland Speicher, Saarland University, Saarbrücken
Michael Schürmann, University of Greifswald
Andreas Thom, TU Dresden
Monika Varso, University of Greifswald
Philip Varso, University of Greifswald
Moritz Weber, Saarland University, Saarbrücken
Sheng Yin, Saarland University, Saarbrücken

Updated: 27 March 2019 Moritz Weber

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