Oberwolfach Reports


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Volume 10, Issue 2, 2013, pp. 1359–1443
DOI: 10.4171/OWR/2013/23

Published online: 2014-03-17

Heat Kernels, Stochastic Processes and Functional Inequalities

Masha Gordina[1], Takashi Kumagai[2], Laurent Saloff-Coste[3] and Karl-Theodor Sturm[4]

(1) University of Connecticut, Storrs, USA
(2) Kyoto University, Japan
(3) Cornell University, Ithaca, United States
(4) Universität Bonn, Germany

The general topic of the 2013 workshop Heat kernels, stochastic processes and functional inequalities was the study of linear and non-linear diffusions in geometric environments: finite and infinite-dimensional manifolds, metric spaces, fractals and graphs, including random environments. The workshop brought together leading researchers from analysis, probability and geometry and provided a unique opportunity for interaction of established and young scientists from these areas. Unifying themes were heat kernel analysis, mass transport problems and related functional inequalities such as Poincar´e, Sobolev, logarithmic Sobolev, Bakry-Emery, Otto-Villani and Talagrand inequalities. These concepts were at the heart of Perelman’s proof of Poincar´e’s conjecture, as well as of the development of the Otto calculus, and the synthetic Ricci bounds of Lott-Sturm-Villani. The workshop provided participants with an opportunity to discuss how these techniques can be used to approach problems in optimal transport for non-local operators, subelliptic operators in finite and infinite dimensions, analysis on singular spaces, as well as random walks in random media.

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Gordina Masha, Kumagai Takashi, Saloff-Coste Laurent, Sturm Karl-Theodor: Heat Kernels, Stochastic Processes and Functional Inequalities. Oberwolfach Rep. 10 (2013), 1359-1443. doi: 10.4171/OWR/2013/23