Karl-Theodor Sturm
Wintersemester 2025/26
- Graduate Seminar on Probability Theory:
Gaussian Free Field and Liouville Quantum Gravity
Di., 14-16 Uhr, Seminarraum 0.007
Vorbesprechung am Mo., 28.07., 12:30 Uhr, Raum 0.006
Abstract:
V5D3 Advanced Topics in Geometry:
Geometric Analysis on Metric Measure Spaces
Di., 10-12 Uhr, und Fr., 12-14 Uhr, Seminarraum 0.006
Beginn: 14. Oktober 2025
The lecture will provide an introduction to the field of geometric analysis on metric
measure spaces which has undergone a vast development and attracted much attention
in recent years. The topics will include:1) Metric spaces: speed of curves, gradient flows, Alexandrov curvature,…
2) Optimal transport: Kantorovich duality, c-convexity, Kantorovich-Wasserstein distances, OT on manifolds,…3) Metric measure spaces: isomorphism, transport and distortion distances, curvature bounds and geodesics in the space of spaces,…
4) Energy: gradient and Cheeger energy on mm-spaces, Dirichlet spaces, examples,…
5) Dirichlet mm-spaces: geometric estimates, transformations, constructions,…
6) Dirichlet mm-spaces of Harnack type: doubling and Poincaré, Gaussian heat kernel estimates, parabolic Harnack inequality,…