Séminaire Orléans

Deformed American footballs satisfy the hot spots conjecture
Chris Judge
Thursday 21 May 2026 14:00 -  Orléans -  Salle de Séminaires

Résumé :

In 1974 Jeffrey Rauch posed the following question: Consider the evolution of heat on a perfectly insulated object. It is well-known that, as time tends to infinity, the temperature distribution will converge to a constant temperature distribution. Rauch asked where the temperature is maximized at very large times. He mused that the `hottest spot' might always drift to the boundary as time limits to infinity.  This `conjecture' appears to be true for simply connected domains in the plane.

We provide a class of domains for which Rauch’s `hot spots conjecture’ is true. 
This talk is based on joint work with Luc Hillairet and Sugata Mondal. 

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