Quantum symmetries of finite graphs

date

15.01.2019 

time

03:00 PM - 04:00 PM 

speaker

Moritz Weber  

affiliation

Uni Saarbrücken 

language

en 

main topic

Mathematics: general

host

Prof. Dr. U. Krähmer  

abstract

In mathematics, symmetries are usually modeled by groups; in modern theories however, we sometimes need to go beyond groups in order to capture symmetry: We need quantum groups.
In this talk, I will briefly motivate and introduce the concept of compact matrix quantum groups by Woronowicz from the 1980's and I will then survey recent developments in the theory of quantum automorphism groups of graphs.
The latter is a very young but promising field initiated by Bichon and Banica about fifteen years ago. Together with my PhD student Simon Schmidt, we showed that the quantum symmetry group of a graph C*-algebra is exactly the quantum automorphism group of the graph, hence the graph C*-algebra preserves the quantum symmetries of the underlying graph. I will also mention a number of open problems and conjectures. Note that most of the actual computations are of a very algebraic nature.

 

• Seminar Geometrie

Last update: 13.12.2018 10:26.