In the last two decades great progress has been made in the study of dispersive and wave equations. Over the years the toolboxused 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 the periodic 2D cubic nonlinear Schrodinger equation. I will start by giving a physical derivation of the equation derived from a quantum many-particles system, I will introduce periodic Strichartz estimates along with some remarkable connections to analytic number theory, I will move on the concept of energy transfer and its connection to dynamical systems, and I will end with some results, such as the non-squeezing theorem, that one can obtain once the equation is viewed in the frequency space as an infinite dimension Hamiltonian system.

The seminar will be held on ZOOM at https://us04web.zoom.us/j/159811279 - Meeting ID: 159 811 279