| Math 290: PDE Learning Seminar (Fall 2020) Wave packets in dispersive PDEs |
| The goal of this learning seminar is to discuss various instances of application of the idea of wave packets in dispersive PDEs. For UC Berkeley students: To enroll in this seminar, please use CCN#15439(26) |
| Schedule |
| In general, we will meet on Wednesdays from 4:10 pm to 5:30 pm at: https://berkeley.zoom.us/j/95756095747 (see the up-to-date syllabus below for the precise schedule). |
| Mailing list & shared files |
If you would like to join the seminar mailing list, please visit: https://groups.google.com/a/lists.berkeley.edu/g/pde-learning-seminar-2020f |
The relevant files will be available at (access restricted to UC Berkeley members): https://drive.google.com/drive/folders/1nF6XJnELNgiCwkhgCvmGwSVu-OHez0Jh?usp=sharing |
| Syllabus (will be updated) | |||
| Date | Topic | Refs. | Speaker |
| 9/23 | Organizational meeting | ||
| 10/7 | Wave packets for constant-coefficient dispersive PDEs | - | Xiaoyu Huang |
| 10/14 | Decay estimate via wave packets for constant-coefficient dispersive PDEs | - | Yuchen Mao |
| 10/21 | Basic phase space analysis via the FBI transform | [1, 2] | Yonah Borns-Weil |
| 10/28 | Wave pacekts for variable coefficient dispersive equations | [3] | Mitchell Taylor |
| 11/4 | Null geometry and wave packets for variable coefficient wave equations | [4] | James Rowan |
| 11/11 | Long time Strichartz estimate on asymptotically flat spacetimes | [5, 6] | Jian Wang |
| 11/18 | Modified scattering for the 1D cubic NLS | [7] | Benjamin Pineau |
| 12/2 | Nash-Kuiper embedding | - | Federico Pasqualottto |
| 12/9 | Bilinear restriction estimates | [8, 9] | Georgios Moschidis |
| References (will be updated) | |
| 1 | D. Tataru Phase space transforms and microlocal analysis |
| 2 | D. Tataru On the Fefferman-Phong inequality and related problems |
| 3 | H. Koch and D. Tataru, Dispersive estimates for principally normal pseudodifferential operators |
| 4 | H. Smith and D. Tataru, Sharp local well-posedness results for the nonlinear wave equation |
| 5 | D. Tataru, Parametrices and dispersive estiamtes for Schrodinger equation with variable coefficients |
| 6 | J. Metcalfe and D. Tataru, Global parametrices and dispersive estimates for variable coefficient wave equations |
| 7 | M. Ifrim and D. Tataru, Global bounds for the cubic nonlinear Schrodinger equation (NLS) in one space dimension |
| 8 | T. Wolff, A sharp bilinear cone restriction estimate |
| 9 | T. Tao, Endpoin bilinear restriction theorems for the cone, and some sharp null form estimates |