Non-commutative Deformation of Moduli Space of Flat Connections on Riemann Surfaces

Explore a 47-minute mathematics lecture delving into the non-commutative deformation of spaces of flat connections on Riemann surfaces, presented by Andras Szenes from the University of Geneva. Learn about the historical development of formal deformations of functions on manifolds from their 1970s introduction as a mathematical approach to quantum mechanics through Fedosov's construction on symplectic manifolds in the mid-1990s. Discover how Maxim Kontsevich's groundbreaking 1997 paper revolutionized the field by incorporating higher algebra and modern quantum physics principles. Gain insights into the philosophical underpinnings and recent developments of research conducted by Szenes and Philippe Roche on deformation of spaces of flat connections on Riemann surfaces.