Graduate Students Geometry and Analysis Seminar
- Event Type
- Seminar/Symposium
- Sponsor
- Department of Mathematics
- Location
- Henry Admin Building 143
- Date
- Sep 15, 2023 2:00 pm
- Speaker
- Ryan McConnell
- Contact
- Hanna Kim
- nekim2@illinois.edu
- Views
- 1
- Originating Calendar
- Graduate Student Seminars in Mathematics
Title: Strichartz Inequalities on Compact Manifolds
Abstract: Strichartz inequalities on Rn follow from a simple dispersion estimate and interpolation, and are optimal. The story changes dramatically on compact domains, where such an estimate can never hold. However, it is a great triumph of Bourgain that intermediate estimates hold at all on the Torus, and the ideas behind his proofs have been a driving force behind much of modern Harmonic Analysis. In this talk we will discuss the case of an arbitrary compact manifold without boundary and develop lossy-Strichartz estimates that somehow end up being sharp on certain manifolds (like the sphere!). This talk is a sequel to a prior talk I gave but won't require any knowledge of the other. Strichartz inequalities on Rn follow from a simple dispersion estimate and interpolation, and are optimal. The story changes dramatically on compact domains, where such an estimate can never hold. However, it is a great triumph of Bourgain that intermediate estimates hold at all on the Torus, and the ideas behind his proofs have been a driving force behind much of modern Harmonic Analysis. In this talk we will discuss the case of an arbitrary compact manifold without boundary and develop lossy-Strichartz estimates that somehow end up being sharp on certain manifolds (like the sphere!). This talk is a sequel to a prior talk I gave but won't require any knowledge of the other.