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URL:https://murmitoyen.com/events/vanille/udem/detail/675076-conferences-ni
 renberg-du-crm-en-analyse-geometrique-gunther-uhlmann-university-of-washin
 gton
LOCATION:Université de Montréal - Pavillon André-Aisenstadt\, 2920\, che
 min de la Tour\, Montréal\, QC\, Canada\, H3T 1N8
SUMMARY:Conférences Nirenberg du CRM en analyse géométrique: Gunther Uhl
 mann (University of Washington)
DESCRIPTION: Cette conférence s'adresse à un large auditoire. This lectu
 re is aimed at a general mathematical audience.
\nCan we make objects invi
 sible? This has been a subject of human fascination for millennia in Greek
  mythology\, movies\, science fiction\, etc. \, including the legend of Pe
 rseus versus Medusa and the more recent Star Trek and Harry Potter. In the
  last decade or so there have been several scientific proposals to achieve
  invisibility. We will introduce some of these in a non-technical fashion 
 concentrating on the so-called 'transformation optics' that has received t
 he most attention in the scientific literature.
\nJourney to the Center of
  the Earth Le lundi 21 mars 2016 à 16h We will consider the inverse probl
 em of determining the sound speed or index of refraction of a medium by me
 asuring the travel times of waves going through the medium. This problem a
 rises in global seismology in an attempt to determine the inner structure 
 of the Earth by measuring travel times of earthquakes. It has also several
  applications in optics and medical imaging among others.
\nThe problem ca
 n be recast as a geometric problem: Can one determine a Riemannian metric 
 of a Riemannian manifold with boundary by measuring the distance function 
 between boundary points? This is the boundary rigidity problem. We will al
 so consider the problem of determining the metric from the scattering rela
 tion\, the so-called lens rigidity problem. The linearization of these pro
 blems involves the integration of a tensor along geodesics\, similar to th
 e X-ray transform.
\nWe will also describe some recent results\, joint wit
 h Plamen Stefanov and Andras Vasy\, on the partial data case\, where you a
 re making measurements on a subset of the boundary. No previous knowledge 
 of Riemannian geometry will be assumed.
\nSeeing Through Space-Time Le mar
 di 22 mars 2016 à 16 h
\nWe consider inverse problems for the Einstein eq
 uation with a time-depending metric on a 4-dimensional globally hyperbolic
  Lorentzian manifold. We formulate the concept of active measurements for 
 relativistic models. We do this by coupling Einstein equations with equati
 ons for scalar fields.
\nThe inverse problem we study is the question of w
 hether the observations of the solutions of the coupled system in an open 
 subset of the space-time with the sources supported in this set determines
  the properties of the metric in a larger domain. To study this problem we
  define the concept of light observation sets and show that knowledge of t
 hese sets determines the conformal class of the metric. This corresponds t
 o passive observations from a distant area of space which is filled by lig
 ht sources.
\nWe will start by considering inverse problems for scalar non
 -linear hyperbolic equations to explain our method. No previous knowledge 
 of Lorentzian geometry or general relativity will be assumed.
\nUne récep
 tion suit la conférence / A reception follows.
\n 
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