Mathematical Conversations

The vision of the sets according to Brownian travelers

The harmonic measure is an important tool, which allows one to reconstruct a harmonic function from its values on the boundary. But it also admits a very simple and beautiful probabilistic interpretation: it is the probability that the path of the Brownian motion originating at a specified point will exit the domain through the given portion of the boundary, in other words, it shows how well a Brownian traveler "sees" certain pieces of the boundary. The relations between the properties of this measure and geometry of the domain and its boundary are deep and mysterious: despite a century of research some questions are still open and some have only been resolved recently. We shall discuss some known connections as well as unsolved problems.

Date & Time

February 02, 2022 | 6:00pm – 8:00pm

Location

Birch Garden, Simons Hall

Affiliation

University of Minnesota

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