Research Interests

I would categorize my research as “physical mathematics”, broadly on the interface of number theory, geometry, physics and computation, mostly from an analytic and arithmetic perspective.

As a physicist, I am interested in:

  1. Construction and characterization of rational conformal field theories with moduli spaces
  2. Enumerative BPS invariants in string theory (ex: BPS black hole entropy, wall crossing etc.)
  3. Arithmetic and motivic structures underlying Feynman integrals

As a mathematician, I am interested in:

  1. Mathematical structure of attractor varieties
  2. Applications of automorphic and analytic L functions
  3. Automorphic forms for groups of higher ranks & Geometric theory of automorphic forms
  4. Arithmetic statistics of elliptic curves and surfaces
  5. Cryptography
  6. Computational methods of Calabi-Yau geometry and arithmetic