Research

I am primarily interested in several complex variables (SCV), complex geometry, CR geometry, partial differential equations. I am also actively working on theoretical problems in machine learning and mathematical physics.

Below, you'll find my research organised by publication type and year. For questions on any specific publication, feel free to email me.

1. Bergman-Einstein metrics on two-dimensional Stein spaces, 2022. [ArXiv preprint]. Joint with Shubham Sinha.
   Accepted in Michigan Mathematical Journal. 

2. Local algebraicity and localization of the Bergman kernel on Stein spaces with finite type boundaries, 2024. [ArXiv preprint].
   Joint with Peter Ebenfelt and Ming Xiao.
   Accepted in Indiana University Mathematics Journal. 

3. Rotational symmetries of domains and Bergman space monomials, 2024. [ArXiv preprint].
   Joint with John N. Treuer.
   Accepted in Journal of Mathematical Analysis and Applications. 

4. Abundance of Bergman metrics with constant positive holomorphic sectional curvature, 2026. [Arxiv preprint].
   Joint with Ming Xiao, Shreedhar Bhat, Achinta Kumar Nandi.

5.  Cohomology of complex supertori, 2026. [Arxiv preprint].
   Joint with Hargun Bhatia, Zhiyuan Jiang, Jeffrey M Rabin, Steven V Sam.

1. Uniform C^k Approximation of G-Invariant and Antisymmetric Functions, Embedding Dimensions, and Polynomial Representations, 2024. [ArXiv preprint].
   Joint with Rahul Sarkar, Khoa Tran. 

2. Attention as In-Context Empirical Bayes: A Two-Stage View via Particle Dynamics, 2026. [ArXiv preprint].
   Joint with Matthew Smart, Nilava Metya, Alexandre V. Morozov, Anirvan M. Sengupta.