Interests: general relativity, AdS/CFT (+ quantum field theory/strings in general), geometric analysis
Contact me: nikhil.chakraborty@stonybrook.edu
Advisor: Marcus Khuri
Disclaimer: These notes reflect my understanding of these topics, which still needs quite a bit of work. I presented some of this stuff in our Student Mathematical Physics Seminar (which I organized), and our Advanced Graduate Theory Seminar.
Introduction to quantum field theory, momentum space Feynman rules (supplement). Mostly basic perturbation theory with scalars and no gauge symmetry. Main source: Peskin and Schroeder.
Hawking radiation on a Vaidya spacetime. This derivation does not discuss the universality of the radiation spectrum -- it just provides a specific example. Source: this paper; I just wrote out the calculations in some more detail.
Stringy black holes
Some perspectives on apparent horizons
Jang equation and positive mass theorem (following Schoen-Yau '81)
Supersymmetry, mass, and the BPS condition (starting with Witten '81)
Mass functionals in GR
Seiberg-Witten geometry and N = 2 SUSY
Calabi-Yau compactifications (heterotic strings, then Type IIA/IIB strings)