Workshop on Representation Theoretical and Categorical Structures in Quantum Geometry and Conformal Field Theory

Photograph by Martina Lanini

Manifold invariants constructed from the representation categories of Hopf algebras and from more general tensor categories play an important role in quantum geometry, conformal field theory, representation theory and topological field theory.

The workshop aims to bring together scientists from these disciplines to encourage interaction and to develop a common language across the boundaries of these subjects. Within these three main subjects, the thematic focus will be on the following research topics:

• Quantum geometry and quantum gravity:
  state sum models, quantum group representations in quantum geometry, models involving (higher) categories, 2-groups in quantum geometry, inclusion of matter and observables.


• (Higher) categories and (extended) TFTs:
  discrete models involving higher categories, relation between Turaev-Viro and Reshetikhin-Turaev invariants, categorical structures and higher TFTs.


• Representation theoretical structures inspired by rational CFT:
  module categories, categorical center, chiral theories as a three-category.

• Benjamin Balsam, Stony Brook
• John Barrett, University of Nottingham
• Christoher Douglas, University of Oxford
• Jürgen Fuchs, Karlstad University
• Winston Fairbairn, FAU Erlangen-Nürnberg
• Krzysztof Gawędzki, ENS Lyon
• Liang Kong, Tsinghua University
• Marco Mackaay, Algarve University
• Shahn Majid, Queen Mary University
• Jeffrey Morton, IST, Lisbon
• Michael Müger, University of Nijmegen
• Thomas Nikolaus, University of Regensburg
• Karim Noui, Université de Tours
• Victor Ostrik, University of Oregon
• Hendryk Pfeiffer, UBC
• Roger Picken, IST, Lisbon
• Ingo Runkel, Hamburg University
• Urs Schreiber, Utrecht University
• Rafal Suszek, University of Warsaw
• Alexis Virelizier, Université Montpellier 2
• Derek Wise, FAU Erlangen-Nürnberg

For each of the main topics there will be two introductory talks (1h each) which give an in-depth presentation of the subject as well as several talks covering specific aspects of the topic (1 h) and shorter contributions (30 min). All talks will be aimed at a mixed audience of mathematicians and physicists and emphasize the connections to the other fields. For the schedule and more detailed information on the talks, see our programme page

The workshop will take place in Erlangen, which is a university town in the south-east of Germany in the region of Franconia. It is easy to reach by a combination of air and train travel. For detailed travel instructions, see our travel and directions page.

The workshop location is the Kollegienhaus, Universitätsstraße 15, 91054 Erlangen of the University of Erlangen-Nürnberg (Map). It is located in the city centre of Erlangen, close to the train station and borders on the historical castle garden.

This workshop is funded by the ESF Research Networking Programme "Quantum Geometry and Quantum Gravity" and by the Priority Programme 1388: Representation Theory of the German Research Foundation (DFG). We express our gratitude for their support.