Notes
(Just a very rough attempt to provide some organization.)
Below is a listing of some random notes that I don't mind making available for public consumption, in reverse chronological order.
There is a search box with a very rudimentary search function (exact phrase matching only).
| Title | Venue/Year | Keywords | Link |
|---|---|---|---|
| Some interpolation inequalities | (2023) | PDE, analysis, Holder space, Sobolev space | |
| Mathematical General Relativity: Evolutionary and Causal Aspects | NCTS, Taiwan (2023, 2024) | general relativity, lecture notes | PDF (Draft, changes frequently; includes also notes for the Spring 2024 course) |
| Geodesic congruences | (2023) | differential geometry, general relativity, geodesic congruence, bundles, connection, null structure | |
| Compactness and Non-compactness | MTH849 (2022) | PDE, analysis, concentration compactness, Sobolev embedding | |
| Derivatives: a geometric supplement | (2015) | differential geometry, connection, bundles | |
| Approximating Continuous Functions | (2013) | Weierstrass approximation, Runge's Phenomenon, Bernstein polynomial | |
| Lecture Notes on Sobolev Spaces | CCA (2011) | PDE, analysis, Sobolev spaces | |
| How to derive the Kerr metric by cheating quite a bit | MAT 451 (2009) | General relativity, Kerr |