Wojciech J. Gajda

Abstract: I will start with an introduction to quantum graphs, which are graph-like objects modelled on noncommutative algebras. I will try to highlight the more algebraic/categorical aspects of the theory. In the second half of the talk I will present two results about symmetries, both analogues of well-known results for graphs. The first one says that generic quantum graphs do not have any (quantum) symmetries. The second one says that any finite (quantum) group can be realised as the quantum automorphism group of some quantum graph, which is a noncommutative counterpart of Frucht's theorem. Both of these results involve (compact) quantum groups, so I will devote some time to introduce these objects as well.