Frucht's Theorem for Finite Quantum Groups

This lecture from the BIMSA-Tsinghua Quantum Symmetry Seminar features Mateusz Wasilewski from the Institute of Mathematics of the Polish Academy of Sciences discussing Frucht's theorem for finite quantum groups. Explore how the classical Frucht's theorem, which states that every finite group can be realized as an automorphism group of a finite graph, extends to quantum groups. Learn why the direct analogue fails for finite quantum groups, as shown by Banica and McCarthy, and discover the alternative approach using quantum graphs that successfully proves every finite quantum group is the quantum automorphism group of a finite quantum graph. Examine the question of when a quantum Cayley graph can be found whose quantum automorphism group is the original finite quantum group, with particular focus on duals of classical groups. The presentation references joint work with Michael Brannan, Daniel Gromada, Junichiro Matsuda, and Adam Skalski, with slides and video available on the BIMSA website.