Heat kernels, stochastic processes and functional inequalities. Abstracts from the workshop held May 5--11, 2013.
type: Item
instance of: scholarly article
title: Heat kernels, stochastic processes and functional inequalities. Abstracts from the workshop held May 5--11, 2013.
zbMATH Open document ID: 1349.00173
DOI: 10.4171/OWR/2013/23
published in: Oberwolfach Reports
publication date: 2016-11-27T00:00:00Z
review text: Summary: The general topic of the 2013 workshop \textit{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 Poincaré, Sobolev, logarithmic Sobolev, Bakry-Emery, Otto-Villani and Talagrand inequalities. These concepts were at the heart of Perelman's proof of Poincaré'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.
Mathematics Subject Classification ID: 00B05
Mathematics Subject Classification ID: 00B25
Mathematics Subject Classification ID: 58-06
Mathematics Subject Classification ID: 58J65
Mathematics Subject Classification ID: 58J35
Mathematics Subject Classification ID: 60J45
Mathematics Subject Classification ID: 60K37
Mathematics Subject Classification ID: 60F17
Mathematics Subject Classification ID: 53C23
zbMATH DE Number: 6656886
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 6656886