Topics in Mathematical Physics I

This is a graduate seminar that uses general relativity as a working language for cosmology, treating Einstein's equations less as a finished theory and more as a flexible framework you can stretch — into FLRW spacetimes, inflation, and modified gravity like f(R). You'll review the geometric machinery (Killing vectors, the gravitational action, the energy-momentum tensor), then spend most of the term building and solving cosmological models, with regular homework and two midterms keeping the calculations honest. It sits at the interface where differential geometry, PDE symmetry methods, and observational cosmology meet, and is the natural launching point if you want to do research in gravitation or theoretical cosmology.