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SUMMARY:Recent Progress in the Hot Spots Conjecture - Jaume de Dios Pont (
 ETH Zürich)
DTSTART:20260225T110000Z
DTEND:20260225T120000Z
UID:TALK245086@talks.cam.ac.uk
DESCRIPTION:As time evolves\, the temperature in a homogeneous\, well insu
 lated 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 boun
 dary 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 man
 y 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 fal
 se\, including the class of convex sets\, and how to find the exact value 
 of this ratio in every dimension.
LOCATION:Seminar Room 2\, Newton Institute
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