Göran Gustafsson Lectures in Mathematics

GÖRAN GUSTAFSSON Lectures in Mathematics

May 18 - 22, 2018
KTH, Stockholm

Gigliola Staffilani
Massachusetts Institute of Technology, Cambridge

Abstracts:

Lecture 1: The many faces of dispersive equations
Friday, May 18, 1.15-2.15 pm
Lecture hall D2, Lindstedtsvägen 17

In recent years 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 variety of techniques from Fourier and harmonic analysis, analytic number theory, math physics, dynamical systems, probability and symplectic geometry. In this talk I will introduce a variety of problems connected with dispersive and wave equations, such as the derivation of a certain nonlinear Schrodinger equations from a quantum many-particles system, periodic Strichartz estimates, the concept of energy transfer, the invariance of a Gibbs measure associated to an infinite dimension Hamiltonian system and non-squeezing theorems for such systems when they also enjoy a symplectic structure.

Coffee is served between 12.45 and 13.15 outside the lecture hall.

Lecture 2: Strichartz Estimates: The dance between analytic number theory and harmonic analysis
Monday, May 21, 1.15-2.15 pm
Lecture hall D3, Lindstedtsvägen 17

In this second lecture I will zoom into the rich mathematics behind the proofs of Strichartz estimates. As mentioned in the first lecture these estimates are fundamental in order to prove well-posedness of dispersive initial value problems by assuming only boundedness of the mass and energy of the initial data. In recent years, while looking for a proof of Strichartz estimates in the periodic setting, a much deeper connection than previously anticipated has been found between analytic number theory and harmonic analysis. I will describe in general terms this connection throughout the lecture.

Lecture 3: On long time instability of the zero solution to certain Nonlinear Schrodinger equations
Tuesday, May 22, 1.15-2.15 pm
Lecture hall E3, Osquars backe 14

The aim of this third lecture is to analyze the long time instability of the zero solution of the 2D periodic defocusing cubic NLS, while outlining the differences between the dynamics on rational versus irrational tori. In particular we will analyze the structure of the resonance sets in these two different set ups. This instability can also be related to well known phenomena such as energy transfer and forward cascades.

Sponsored by the Göran Gustafsson Foundation

2018-05-08