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UID:20251219T105745EST-3554Pd94Ue@132.216.98.100
DTSTAMP:20251219T155745Z
DESCRIPTION:Conférence Nirenberg du CRM en analyse géométrique: Can one hea
 r the shape of a drum and deformational spectral rigidity of planar domain
 s\n\nWeb site : http://www.crm.math.ca/Nirenberg2019/\n\nM. Kac popularize
 d the following question 'Can one hear the shape of a drum?'. Mathematical
 ly\, consider a bounded planar domain $Omega subset mathbb R^2$ with a smo
 oth boundary and the associated Dirichlet problem $Delta u+lambda u=0\, u|
 _{partial Omega}=0$. The set of $lambda$'s for which this equation has a s
 olution is called the Laplace spectrum of $Omega$. Does the Laplace spectr
 um determine $Omega$ up to isometry? In general\, the answer is negative.
 \n	\n	Consider the billiard problem inside $Omega$. Call the length spectrum
  the closure of the set of perimeters of all periodic orbits of the billia
 rd inside $Omega$. Due to deep properties of the wave trace function\, gen
 erically\, the Laplace spectrum determines the length spectrum. We show th
 at a generic axially symmetric domain is dynamically spectrally rigid\, i.
 e. cannot be deformed without changing the length spectrum. This partially
  answers a question of P. Sarnak. The talk is a based on two separate join
 t works with J. De Simoi\, Q. Wei and with J. De Simoi\, A. Figalli.\n
DTSTART:20190123T200000Z
DTEND:20190123T210000Z
LOCATION:Room 5345\, CA\, Pav. André-Aisenstadt
SUMMARY:Vadim Kaloshin\, University of Maryland
URL:/mathstat/channels/event/vadim-kaloshin-university
 -maryland-293439
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