Research

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

Prior Work

My PhD dissertation was on Automorphic Forms in String Theory. My PhD supervisors were Timm Wrase and Anton Rebhan.

During my PhD and a few years that followed, I worked on problems in combinatorial enumerative geometry of CY manifolds and K3 surfaces with applications to BPS state counts and wall crossing, black holes in string theory, moonshine, vertex operator algebras, and Hodge theory of rational superconformal field theories.

Current Work

These days, I am interested in the following mathematical topics:

• Computational aspects of the Langlands program. This includes:
  • Computing of automorphic and analytic L functions and zeta functions
  • Arithmetic statistics and distributions of traces of Frobenius (Sato-Tate, Lang-Trotter)
  • Computational methods for Calabi-Yau varieties and motives, and their arithmetic
• Theory of automorphic forms (Mock, Real Analytic, Siegel, Hilbert, Exceptional, Bianchi)
• Theory of complex multiplication of abelian varieties, its generalizations to algebraic varieties

and how can be applied to/studied from the following areas of physics and computing:

• Mathematical structure of attractor varieties
• Construction and characterization of rational conformal field theories with moduli spaces
• Enumerative geometry and phenomena like wall crossing, conifold transisitons, flops, jumping
• Arithmetic and motivic structures underlying Feynman integrals
• Cryptography

I have also been recently working on and studying the algebraic geometry and number theory of game theory.