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UID:69d9fb378f7cf
DTSTAMP:20260411T034143
DTSTART:20190122T150000
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DTEND:20190122T150000
URL:https://murmitoyen.com/events/vanille/udem/detail/861213-birkhoff-conje
 cture-for-convex-planar-billiards
LOCATION:Université de Montréal - Pavillon André-Aisenstadt\, 2920\, che
 min de la Tour\, Montréal\, QC\, Canada\, H3T 1N8
SUMMARY:Birkhoff Conjecture for convex planar billiards
DESCRIPTION:Conférence Nirenberg en analyse géométrique
\nConférence de
  Vadim Kaloshin\, titulaire de la chaire Michael Brin en mathématiques de
  l'Université du Maryland. Il a obtenu son doctorat de l'Université de P
 rinceton en 2001 sous la supervision de John Mather. Le professeur Kaloshi
 n a apporté des contributions fondamentales à la théorie des systèmes 
 dynamiques\, notamment à l'étude de la diffusion d'Arnold\, du problème
  à n corps et de la conjecture de Birkhoff pour le billard convexe.
\nRé
 sumé:G.D. Birkhoff introduced a mathematical billiard inside of a convex 
 domain as the motion of a massless particle with elastic reflection at the
  boundary. A theorem of Poncelet says that the billiard inside an ellipse 
 is integrable\, in the sense that the neighborhood of the boundary is foli
 ated by smooth closed curves and each billiard orbit near the boundary is 
 tangent to one and only one such curve (in this particular case\, a confoc
 al ellipse). A famous conjecture by Birkhoff claims that ellipses are the 
 only domains with this property. We show a local version of this conjectur
 e —namely\, that a small perturbation of an ellipse has this property on
 ly if it is itself an ellipse. This is based on several papers with A. Avi
 la\, J. De Simoi\, G. Huang and A. Sorrentino.
\n 
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