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SUMMARY:Gigliola Staffilani (MIT)
DTSTART:20210506T153000Z
DTEND:20210506T163000Z
DTSTAMP:20260423T040036Z
UID:SIAM-PDE/10
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/SIAM-PDE/10/
 ">How much math do you need to know to “solve" an initial value problem?
 </a>\nby Gigliola Staffilani (MIT) as part of Seminar In the Analysis and 
 Methods of PDE (SIAM PDE)\n\n\nAbstract\nIn this talk I will present some 
 recent results concerning periodic solutions to nonlinear Schrodinger equa
 tions\, and in doing so I will introduce a variety of mathematical techniq
 ues that range from harmonic and Fourier analysis to dynamical systems\, f
 rom number theory to probability. \n\nI will start with a derivation of th
 is type of equation from a many body system\, and I will discuss how Hamil
 tonian structures can be mapped through this derivation process. I will th
 en move to the study of the long time dynamics of associated initial value
  problems\, in particular I will concentrate on the notion of energy trans
 fer. I will show how ideas from dynamical systems are fundamental to work 
 through this analysis to obtain even  relatively soft statements\, and I w
 ill present some more recent results on the rigorous derivation of a wave 
 kinetic equation for a certain multidimensional KdV type equation using a 
 variety of tools such as Feynman diagrams\, sharp dispersive estimates and
  improved combinatorial lemmata.\n
LOCATION:https://researchseminars.org/talk/SIAM-PDE/10/
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