Nick Chakraborty, 2nd year math PhD student at Stony Brook

Interests: general relativity, AdS/CFT (+ quantum field theory/strings in general), geometric analysis

Contact me: nikhil.chakraborty@stonybrook.edu

Advisor: Marcus Khuri

Pedagogical Notes

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, and our Advanced Graduate Theory Seminar.

Physics

Introduction to quantum field theory

Thermodynamics of black holes

Stringy black holes

Some perspectives on apparent horizons

Math

Jang equation and positive mass theorem (following Schoen-Yau '81)

Supersymmetry, mass, and the BPS condition (starting with Witten '81)

In-Between

Mass functionals in GR

Seiberg-Witten geometry and N = 2 SUSY

BRST quantization

Calabi-Yau compactifications (heterotic strings, then Type IIA/IIB strings). SYZ mirror conjecture is stated.

Axiomatic TQFTs. Also, basics of topological twists.