BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Hadewijch De Clercq (Ghent University\, Belgium) DTSTART:20211129T150000Z DTEND:20211129T160000Z DTSTAMP:20260422T175700Z UID:QGS/44 DESCRIPTION:Title: Dyn amical quantum graphical calculus\nby Hadewijch De Clercq (Ghent Unive rsity\, Belgium) as part of Quantum Groups Seminar [QGS]\n\n\nAbstract\nGr aphical calculus provides a diagrammatic framework for performing topologi cal computations with morphisms in strict tensor categories. The key idea is to identify such morphisms with oriented diagrams labeled by their in- and output objects. This was formalized by Reshetikhin and Turaev\, by con structing for every strict tensor category $C$ a strict tensor functor tha t assigns isotopy classes of $C$-colored ribbon graphs to morphisms in $C$ . This can be applied to the tensor category of finite-dimensional represe ntations of a quantum group $U_q(g)$.\n\nIn this talk\, I will first outli ne the fundamentals of this finite-dimensional quantum graphical calculus. Then I will explain how it can be extended to a larger category of quantu m group representations\, encompassing the quantum group analog of the BGG category $O$. In particular\, this extended framework allows to visualize $U_q(g)$-intertwiners on Verma modules\, as well as morphisms depending o n a dynamical parameter\, such as dynamical R-matrices. Finally\, I will d escribe how this dynamical quantum graphical calculus can be used to obtai n q-difference equations for quantum spherical functions.\n\nThis talk is based on joint work with Nicolai Reshetikhin (UC Berkeley) and Jasper Stok man (University of Amsterdam)\n LOCATION:https://researchseminars.org/talk/QGS/44/ END:VEVENT END:VCALENDAR