Hot spots conjecture and critical points of Neumann eigenfunctions of polygonal planar domains
Analysis and Geometry Seminar
29th October 2020, 3:15 pm – 4:15 pm
Online, (contact organisers for details)
Suppose a flat piece of metal (represented by a two-dimensional bounded connected domain) is given an initial heat distribution which then flows throughout the metal. Assume that the metal is insulated, which means that no heat escapes from the piece of metal. The hot spots conjecture says that the hottest and coldest points on the metal lie close to its boundary after sufficient amount of time. I will try to elaborate on the mathematical formulation of this conjecture and provide some history and recent results.