Monday, March 10 2025.
Day 1 - Monday, March 10th
Dispersive waves. Linear Schrödinger equation. Fundamental solution. Time decay. Non endpoint Strichartz estimates.
Program
Wednesday, March 12 2025.
Day 2 - Wednesday, March 12th
Endpoint Strichartz estimates (Keel-Tao).
Friday, March 14 2025.
Day 3 - Friday, March 15th
H^1-subcritical NLS: Local Cauchy Theory by compactness arguments. Global Cauchy theory in the defocusing case.
Monday, March 17 2025.
Day 4 - Monday, March 17th
Focusing H^1-subcritical NLS: Global Cauchy Theory. Gagliardo-Nirenberg inequalities, Virial Theorem. Blow-up á la Glassey.
Wednesday, March 19 2025.
Day 5 - Wednesday, March 19th 9:30 - 11:30
Scattering for NLS. Existence and asymptotic completeness of Wave Operators. Morawetz estimates. Interaction Morawetz estimates. Pseudoconformal transformation.
Monday, March 24 2025.
Day 7 - Monday, March 24th
The Kenig-Merle Strategy.
Wednesday, March 26 2025.
Day 8 - Wednesday, March 26th
The Kenig-Merle Strategy.
Friday, March 28 2025.
Day 9 - Friday, March 28th
The Kenig-Merle Strategy.
Monday, March 31 2025.
Day 10 - Monday, March 31st
The Kenig-Merle Strategy.
Wednesday, April 02 2025.
Day 11 - Wednesday, April 2nd
Linear Schrödinger equation with potentials. Subcritical potentials, time-decay and Strichartz estimates.
Friday, April 04 2025.
Day 12 - Friday, April 4th
Scaling critical potentials: Strichartz estimates and time-decay.
Monday, April 07 2025.
Day 13 - Monday, April 7th 10:00 - 12:00
Uncertainty principles 1: Hardy inequalities and applications.
Wednesday, April 09 2025.
Day 14 - Wednesday, April 9th
Uncertainty principles 2: dynamical uncertainty.
Friday, April 11 2025.
Day 15 - Friday, April 11th
Spectral stability. Embedded eigenvalues. Mourre Theory, Birman-Schwinger Principle, method of multipliers. Eigenvalue localization (Sobolev inequalities, Birman-Schwinger).