# Quantum groups and their analysis

Summer school and workshop at University of Oslo

This program is supported by «Pure Mathematics in Norway» by Bergen Research Foundation with the collaboration of the Tromsø Research Foundation.

The theory of quantum groups has been a curious meeting point of analysis and algebra since its inception, and it provides powerful guiding principles in mathematics and mathematical physics. Historically, the formalism of representing symmetry by groups led to many groundbreaking discoveries in pure and applied mathematics to understand various structures. However, the developments of modern mathematics and quantum physics revealed the need to go beyond that framework in order to capture a new kind of symmetry hidden from plain sight. This led to the birth of quantum groups in the 1980's by Drinfeld and Jimbo among others from algebraic study of quantum integrable systems, and Woronowicz from an operator algebraic study of quantized spaces. About 30 years after the advent, the interplay between these different approaches still provides new viewpoints leading to surprising new results. Moreover, the theory of tensor categories is deeply linked with the representation theory of quantum groups, but also with other fields such as quantum field theory and subfactor theory.

To this end we organize a summer school and a workshop at University of Oslo with distinguished international lecturers.

## Summer school

The aim of this summer school is to help young scientists familiarize with, and start working on problems in the above mentioned fields. The main lecture series are given by four leading researchers in these fields.

- Period: July 29–August 2, 2019
- Location: University of Oslo (the precise location will be announced later)
- Lectures:
- Loïc Foissy (l'Université du Littoral Côte d'Opale): Combinatorial Hopf algebras and operads
- David Jordan (The University of Edinburgh): Morita theory for tensor categories
- Ulrich Krähmer (Technische Universität Dresden): Hopf algebras
- Christian Voigt (The University of Glasgow): Locally compact quantum groups

## Workshop

The workshop aims at bringing together experts from all over the world in the domains of (locally) compact quantum groups, Hopf algebras and tensor categories. As described above, investigating the interplay of these three fields is of high importance for the development of quantum groups in general and the workshop is supposed to support this development.

We encourage the participants of the summer school to stay for the workshop too, in order to get in contact with researchers in the field.

- Period: August 5–9, 2019
- Location: University of Oslo (the precise location will be announced later)
- Speakers: we will add a few more talks, to be announced shortly.
- Martina Balagovic (Newcastle University)
- Gabriella Böhm (Wigner Research Centre for Physics)
- Arnaud Brothier (University of New South Wales)
- Alexandru Chirvasitu (University at Buffalo)
- Jason Crann (Carleton University)
- Loïc Foissy (l'Université du Littoral Côte d'Opale)
- Mehrdad Kalantar (University of Houston)
- Simon Lentner (University Hamburg)
- Yuri I. Manin (Max Planck Institute for Mathematics)
- Ehud Meir (University of Aberdeen)
- Alexander Shapiro (The University of Edinburgh)
- Adam Skalski (Institute of Mathematics, Polish Academy of Sciences)
- Alexander Stottmeister (University of Münster)
- Christian Voigt (The University of Glasgow)
- Jonas Wahl (Universtät Bonn)

## Registration

Registration is open now, until May 1, 2019. There is no conference fee.