Computability of Harmonic Measure

Abstract: We will review recent results relating the geometry of a connected domain to the computability of its harmonic measure at a given point x. In particular, we will discuss examples of domains whose harmonic measure at x is always computable relative to x, but not uniformly. As a by-product, this construction produces "natural" examples of harmonic functions arising as solutions to a Dirichlet problem which are piecewise computable (i.e. all their values are computable relative to the input point), but not computable. This is a work in collaboration with I. Binder, A. Glucksam and M. Yampolsky.

logic

Audience: researchers in the topic

Computability theory and applications

Series comments: Description: Computability theory, logic

The goal of this endeavor is to run a seminar on the platform Zoom on a weekly basis, perhaps with alternating time slots each of which covers at least three out of four of Europe, North America, Asia, and New Zealand/Australia. While the meetings are always scheduled for Tuesdays, the timezone varies, so please refer to the calendar on the website for details about individual seminars.