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SUMMARY:Philippe Charron (Technion)
DTSTART:20211215T121000Z
DTEND:20211215T133000Z
DTSTAMP:20260423T004911Z
UID:GDS/45
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GDS/45/">Ple
 ijel's theorem for Schrödinger operators</a>\nby Philippe Charron (Techni
 on) as part of Geometry and Dynamics seminar\n\n\nAbstract\nWe will discus
 s some recent results regarding the number of nodal domains \nof Laplace a
 nd Schrödinger operators. Improving on Courant's seminal work\, \nPleijel
 's original proof in 1956 was only for domains in R^2 with Dirichlet \nbou
 ndary conditions\, but it was later generalized to manifolds (Peetre and \
 nBérard-Meyer) with Dirichlet boundary conditions\, then to planar domain
 s with \nNeumann Boundary conditions (Polterovich\, Léna)\, but also to t
 he quantum \nharmonic oscillator (C.) and to Schrödinger operators with r
 adial potentials \n(C. - Helffer - Hoffmann-Ostenhof). In this recent work
  with Corentin Léna\, \nwe proved Pleijel's asymptotic upper bound for a 
 much larger class of \nSchrödinger operators which are not necessarily ra
 dial. In this talk\, I will \nexplain the problems that arise from studyin
 g Schrödinger operators as well \nas the successive improvements in the m
 ethods that led to the current results.\n
LOCATION:https://researchseminars.org/talk/GDS/45/
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