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Department of Applied Mathematics and Theoretical Physics

As time evolves, the temperature in a homogeneous, well insulated object evens out, and converges to the initial average temperature in the object. Which points in the material take the longest to reach this equilibrium? In 1974 Rauch conjectured that these slowest points are the ones furthest from the bulk of the material, that is, points in the boundary of the object. This is known as the Hot Spots conjecture.In the last few years our understanding of the conjecture has increased considerably. We now know, for example, that the conjecture has counterexamples in many natural classes of domains. For these classes, we can also quantify how false the conjecture is: Steinerberger introduced the Hot Spots ratio as a natural way to measure the degree of failure of the conjecture. In this talk we will discuss some classes in which the Hot Spots conjecture is false, including the class of convex sets, and how to find the exact value of this ratio in every dimension.

Further information

Time:

25Feb
Feb 25th 2026
11:00 to 12:00

Venue:

Seminar Room 2, Newton Institute

Speaker:

Jaume de Dios Pont (ETH Zürich)

Series:

Isaac Newton Institute Seminar Series