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UID:1068@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20160209T110000
DTEND;TZID=Europe/Paris:20160209T120000
DTSTAMP:20160125T100000Z
URL:https://www.i2m.univ-amu.fr/evenements/does-diffusion-determine-the-dr
 um/
SUMMARY: (...): Does diffusion determine the drum?
DESCRIPTION:: The famous question of Kac is whether one can hear the shape 
 of a drum. Or more precisely\, whether all eigen frequencies of a drum det
 ermine the drum up to congruency. In general the answer to the latter ques
 tion is negative if one allows polygon shaped drums. The eigen frequencies
  are equal if and only if there exists a unitary operator which maps the L
 aplacian on the first drum onto the Laplacian on the second drum. Equivale
 ntly\, this unitary operator intertwines between the two heat semigroups o
 n the drums. In this talk we discuss what happens if the unitary operator 
 is replaced by an order isomorphism\, i.e.\, if it maps positive functions
  to positive functions. Then that order isomorphism maps positive solution
  of the heat equation on the first drum onto positive solutions on the sec
 ond drum. Phrased differently: the order isomorphism tells that the diffus
 ion on the two drums are the same. Hence the question: if the diffusion on
  two drums is the same\, are they then congruent?
CATEGORIES:Séminaire,Analyse Appliquée
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