Jahrestagung der Deutschen Mathematiker-Vereinigung 2006
Rheinische Friedrich-Wilhelms-Universität Bonn
Minisymposium 24 - Probability and Geometry
Prof. Dr. Shizan Fang
Université de Bourgogne
Institute de Mathématiques
BP 47 870
21078 Dijon, France
Prof. Dr. Alexander Grigor'yan
Fakultät für Mathematik
Universität Bielefeld
Universitätsstr. 25
Postfach 10 01 31
33501 Bielefeld, Germany
Dr. Anton Thalmaier
Département de Mathématiques
Université de Poitiers
Téléport 2 - BP 30179
86962 Futuroscope Chasseneuil Cedex, France

The goal of this special session is to bring together people working in Analysis, Geometry or Probability and to focus on recent developments in Geometric Analysis on Riemannian manifolds, Diffusion processes on fractal and singular spaces, Stochastic differential geometry, Stochastic analysis in infinite dimensions.
It is well-known that Brownian motion and martingales on manifolds or vector bundles connect local and global geometry in an intrinsic way, and that many questions related to the geometry of Laplace operators have a direct probabilistic counterpart. Furthermore probabilistic methods often extend naturally to areas, like singular spaces or infinite dimensional spaces, where standard tools of differential analysis or PDE methods fall short. This Mini-Symposium intends to focus on recent progress in these areas.

Auszug zu diesem Minisymposium aus dem Programmheft (Stand: 15. Juli 2006). Weitere nützliche Informationen rund um die Tagung können der verkürzten Ausgabe des Programmheftes entnommen werden.

Programm (Stand: 07.09.2006):

Donnerstag Übungsraum 3, Geographisches Institut, Meckenheimer Allee 166
14:00-14:45 Roland Friedrich (MPI Bonn)
Diffusions on moduli spaces and generalised Stochastic Loewner Evolutions
14:45-15:30 Shigeki Aida (Osaka)
Semi-classical limit of the bottom of spectrum of a Schrödinger operator on a path space over a compact Riemannian manifold
15:30-16:00 Coffee break
16:00-16:45 Ana Bela Cruzeiro (Lisbon)
On a stochastic Euler equation
16:45-17:30 Feng-Yu Wang (Beijing)
Estimates of the first Neumann eigenvalue and the log-Sobolev constant on non-convex manifolds
17:30-18:15 Fuzhou Gong (Beijing)
Exponential ergodicity, spectral gap, and their applications
Freitag Übungsraum 3, Geographisches Institut, Meckenheimer Allee 166
14:00-14:45 Ichiro Shigekawa (Kyoto)
One dimensional diffusions conditioned to be non-explosive
14:45-15:30 Thierry Coulhon (Cergy)
Large time behavior of heat kernels on forms
15:30-16:00 Coffee break
16:00-16:45 José A. Ramírez (Costa Rica)
Beta ensembles, stochastic Airy spectrum, and a diffusion
16:45-17:30 Peter K. Friz (Cambridge)
Stochastic processes as rough paths and Carnot-Caratheodory geometry
17:30-18:15 Marc Arnaudon (Poitiers)
Gradient estimates for positive harmonic functions, Harnack inequalities and heat kernel estimates on Riemannian manifolds, by stochastic analysis
18:15-19:00 Jinghai Shao (Beijing)
Optimal transportation maps for Monge-Kantorovich problem on loop groups