Heat Conduction in Planar Domains

The goal of this talk is to give an overview of what is known about the problem of heat conduction in planar domains. After describing some of the history, which goes back to the 1966 paper by Mark Kac entitled ``Can one hear the shape of a drum?'', I will discuss several results that have been derived over the years, focussing in particular on the time evolution of the heat content of a planar domain whose boundary is kept at constant temperature. Three types of boundary are of interest:
-- polygonal
-- smooth
-- fractal.
For the latter type certain fractal exponents naturally show up, but it turns out in addition that the time evolution is `irregular' in a sense that will be explained.

Refreshments will be served in Math Annex Room 1115, 3:15 p.m.