JournalsowrVol. 10, No. 2pp. 1359–1443

Heat Kernels, Stochastic Processes and Functional Inequalities

  • Masha Gordina

    University of Connecticut, Storrs, USA
  • Takashi Kumagai

    Kyoto University, Japan
  • Laurent Saloff-Coste

    Cornell University, Ithaca, United States
  • Karl-Theodor Sturm

    Universität Bonn, Germany
Heat Kernels, Stochastic Processes and Functional Inequalities cover

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Abstract

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.

Cite this article

Masha Gordina, Takashi Kumagai, Laurent Saloff-Coste, Karl-Theodor Sturm, Heat Kernels, Stochastic Processes and Functional Inequalities. Oberwolfach Rep. 10 (2013), no. 2, pp. 1359–1443

DOI 10.4171/OWR/2013/23