BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Daniel Gromada (Czech Technical University\, Czechia) DTSTART:20240617T140000Z DTEND:20240617T150000Z DTSTAMP:20260422T181400Z UID:QGS/119 DESCRIPTION:Title: Ca yley graphs: Symmetries\, quantizations\, and duality\nby Daniel Groma da (Czech Technical University\, Czechia) as part of Quantum Groups Semina r [QGS]\n\n\nAbstract\nIn the talk\, we are going to quantize several aspe cts of Cayley graphs. First\, we are going to study quantum symmetries of Cayley graphs of abelian groups. From the classical theory\, it is known t hat the Fourier transform diagonalizes the adjacency matrix of any such Ca yley graph.\nThis can be used to determine the graph's quantum automorphis m group. Secondly\, we are going to show\, how to quantize Cayley graphs o f abelian groups. We obtain a quantum graph by twisting the function algeb ra of the classical one. Finally\, we recall a classical\nconstruction tha t takes a distance regular Cayley graph of an abelian group or\, more gene rally\, a translation association scheme and constructs its dual by applyi ng the Fourier transform. We generalize this construction replacing abelia n groups by arbitrary finite quantum groups.\n LOCATION:https://researchseminars.org/talk/QGS/119/ END:VEVENT END:VCALENDAR