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UID:4083@test.i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20160209T110000
DTEND;TZID=Europe/Paris:20160209T120000
DTSTAMP:20160125T100000Z
URL:https://test.i2m.univ-amu.fr/events/does-diffusion-determine-the-drum/
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 deter
mine the drum up to congruency. In general the answer to the latter questi
on is negative if one allows polygon shaped drums. The eigen frequencies a
re equal if and only if there exists a unitary operator which maps the Lap
lacian on the first drum onto the Laplacian on the second drum. Equivalent
ly\, this unitary operator intertwines between the two heat semigroups on
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 t
o positive functions. Then that order isomorphism maps positive solution o
f the heat equation on the first drum onto positive solutions on the secon
d drum. Phrased differently: the order isomorphism tells that the diffusio
n on the two drums are the same. Hence the question: if the diffusion on t
wo drums is the same\, are they then congruent?
CATEGORIES:Séminaire Analyse Appliquée (AA)
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