Colloquium January 27
Date: Friday January 27
Time: 16:00 to 17:00
Place: 455 McBryde (Commons Room)
Speaker: Dmitry Khavinson of Univ of Arkansas at Fayetteville
Title: Some algebraic aspects of the Dirichlet problem
Abstract
In the recent joint work with S. Bell, P. Ebenfelt and Harold S. Shapiro we
study the Dirichlet problem with rational data on the boundary of a plane
domain. We characterize disks as the only domains for which all solutions of
such boundary value problems are rational. We also characterize simply
connected quadrature domains as the only domains for which solutions of all
such Dirichlet problems are algebraic functions whose singularities are
controlled by those of the Riemann mapping function. We shall discuss the
unexpected relations of these questions with Hilbert's thirteenth problem
and the notion of a "lightning bolt" first introduced by Arnold and
Kolmogorov in the 1950s.
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