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SPEAKER: Prof. Krzysztof Bogdan, Wroclaw University of Technology, Polish Academy of Sciences and Stanford University

TITLE: Jump-type random processes and nonlocal boundary value problems

ABSTRACT: We will discuss estimates of harmonic functions, Green function and heat kernel of the fractional Laplacian and related operators on domains. The results are obtained by analysis of jumps and first exit times from domains for the corresponding Markov processes, most notably for the isotropic

stable Levy process. This will be a survey of results and experience accumulated in the last 15 years by the speaker and collaborators, which may shed some light on Dirichlet conditions for nonlocal operators.

 Refreshments will be available at 3:15 p.m.