Gigliola Staffilani, "The Schrödinger equations as inspiration of beautiful mathematics", Dipartimento di Matematica
Colloquium "Guido Castelnuovo"
Luogo: Aula Picone, Dipartimento di Matematica "G. Castelnuovo"
Oratore: Gigliola Staffilani (Abby Rockefeller Mauze Professor Massachusetts Institute of Technology)
Titolo: The Schrödinger equations as inspiration of beautiful mathematics
Abstract:
In the last two decades great progress has been made in the study of dispersive and wave equations. Over the years the toolbox used in order to attack highly nontrivial problems related to these equations has developed to include a collection of techniques: Fourier and harmonic analysis, analytic number theory, math physics, dynamical systems, probability and symplectic geometry. In this talk I will introduce a variety of results using as model problem mainly the periodic 2D cubic nonlinear Schrödinger equation. I will start by giving a physical derivation of the equation from a quantum many-particles system, energy transfer and its connection to dynamical systems, and I will end with some results following from viewing the periodic nonlinear Schrödinger equation as an infinite dimensional Hamiltonian system.
