Topological geometric and brane quantisation of moduli spaces

par Tim Henke

vendredi 30 janv. 2026, 15:30 → 16:30 Europe/Paris

Fokko du Cloux (Bat. Braconnier)

The fields of Topological Quantum Field Theory (TQFT) and Quantum Topology came from the realisation that QFT is sensitive to the topology of the underlying space(time). Witten's 2+1D Chern−Simons TQFT is still one of the crowning achievements of the field. The development of the mathematical counterpart relies on the geometric quantisation of the moduli space (more accurately: moduli stack) of bundles over a Riemann surface. The topological nature of this construction, which is clear from the physics perspective but well hidden behind the complex curve in the mathematical construction, is witnessed by the Hitchin connection, which identifies the Hilbert spaces obtained for different complex structures. I will discuss my previous work on identifying the Hitchin connection with the KZ connection from conformal field theory, and I will discuss my current work on topologising the string-theoretic brane quantisation of the moduli space of Higgs bundles on a curve.