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Dmitry Khavinson: "Between two truths of the real domain, the easiest and shortest path quite often passes through the complex domain." P. Painleve, 1900. A variation on the theme of analytic continua

Time: Wed 2015-12-02, 15.15 - 16.15

Lecturer: Dmitry Khavinson, University of Southern Florida

Place: Oskar Kleins auditorium, AlbaNova

Schedule

14.00-15.00 Pre-colloquium by Aron Wennman (room FD41 Albanova)
15:15-16:15 Colloquium lecture by Dimitry Khavinson (Oskar Klein Auditorium at Albanova)
16:15-17:00 SMC social get together with refreshments

Abstract

How far does the Newtonian potential of a solid bounded by an algebraic surface extend inside the solid? Why is the celebrated Schwarz reflection principle never discussed in dimensions higher than 2? Why a solution of the heat equation analytic near the origin must be entire for all small times? How does one find singularities of an axially symmetric harmonic function in the ball from the coefficients in its expansion by spherical harmonics? If a line intersects an annulus over two disjoint segments and a harmonic function  vanishes on one, does it have to vanish on the other one?

We shall discuss these questions in the unified light of analytic continuation of solutions to linear analytic pde. The talk will be accessible to undergraduate and graduate students majoring in math, physics and engineering.

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