Introduction to PDE (Fall 2022)

This is a fast movinfg bridge course in moderna Analysis and PDE's for both graduate students and advanced undergraduate students. Here is a list of topics:

1. The world of PDE's.
2. Equations derived by the variational principle.
3. Theory of distributions and Fourier Analysis.
4. Basic Inequalities of Real Analysis.
5. Calderon-Zygmund Theory.
6. Strichatz Inequalities and Bilinear Estimates.
7. Applications to PDE's.

Topics on the Mathematical Theory of Black Holes (Spring 2023)

Will cover various topics concerning the rigidity and stabil;ity of Black Holes.