BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Ángel González-Prieto (Univ. Complutense Madrid) DTSTART:20240618T100000Z DTEND:20240618T110000Z DTSTAMP:20260423T010747Z UID:GPL/38 DESCRIPTION:Title: Cha racter Varieties of Knots\nby Ángel González-Prieto (Univ. Compluten se Madrid) as part of Geometry and Physics @ Lisbon\n\nLecture held in 6.2 .33 (Seminar Room\, Math\, FCUL).\n\nAbstract\nKnot invariants\, such as t he Jones polynomial and the Reshetikhin-Turaev invariants\, are ubiquitous in the study of 3-manifold geometry. Among these invariants\, one stands out: the fundamental group of the complement of the knot\, also known as t he knot group. Particularly interesting is the study of the space of repre sentations of these knot groups\, referred to as the character varieties o f knots. Even the simplest properties of these character varieties have le d to profound results in hyperbolic geometry. However\, general methods to uncover the deep geometric features of these spaces are still lacking.\n\ nIn this talk\, we will discuss various aspects of these character varieti es from both geometric and algebraic perspectives. Even for character vari eties of torus knots\, intriguing features emerge that allow us to compare their geometry in both the complex and real cases. Time permitting\, we w ill also explore how Topological Quantum Field Theories can be employed to provide unexpected generalized skein relations for the arithmetic of char acter varieties of knots over finite groups.\n LOCATION:https://researchseminars.org/talk/GPL/38/ END:VEVENT END:VCALENDAR