Research

My research lies broadly in theoretical computer science. I am interested in understanding the limits of efficient computation, especially through communication complexity, extremal combinatorics, and the query complexity of sampling.

Communication complexity and extremal combinatorics

I study combinatorial structures that arise in communication complexity and related areas. A recurring theme is to understand how specific set properties constrain large set systems, and how such structural results can be used to prove lower bounds / upper bounds on the size of set systems. Some concrete (very ambitious) problems include: the (weighted) union-set conjecture, the sunflower conjecture, the Sidorenko conjecture and others.

Sampling and diffusion models

I am interested in the computational and information-theoretic foundations of sampling, especially score-based diffusion models. Questions I think about include the power of exact versus approximate score access, how information is revealed across different noise levels, and what resources are necessary to generate an accurate sample given access to score function queries.

Parallel algorithms and query complexity

I am also interested in the role of adaptivity in sampling and optimization. In particular, I study whether sequential algorithms can be parallelized when many oracle queries are allowed in each round, and what lower bounds prevent further parallelization.

Other interests

My broader interests include proof complexity, randomized algorithms, convex geometry, and high-dimensional probability.