Research

I am broadly interested in Mathematics and Theoretical Computer Science. I enjoy working on problems at the intersection of multiple areas of Math and TCS, such as:

• Algebraic Geometry

• Commutative Algebra

• Combinatorics

• Computational Complexity Theory

• Coding Theory

• Number Theory

I like to view problems through an algebraic-geometric lens and I am excited about developing algebraic-geometric techniques to solve problems in TCS and other areas of Mathematics.

Papers

• Robust Local Testability of Tensor Products of Constant-Rate Algebraic Geometry Codes,

with Sumegha Garg,

66th IEEE Symposium on Foundations of Computer Science, FOCS 2025.

• Rank Bounds and PIT for Σ3ΠΣΠd circuits via a non-linear Edelstein-Kelly theorem,

with Abhibhav Garg and Rafael Oliveira,

66th IEEE Symposium on Foundations of Computer Science, FOCS 2025.

[ECCC] [arXiv]

• Uniform Bounds on Product Sylvester-Gallai Configurations,

with Abhibhav Garg and Rafael Oliveira, 

41st International Symposium on Computational Geometry SoCG 2025. [ECCC]

• Strong Algebras and Radical Sylvester-Gallai Configurations, 

with Rafael Oliveira, 

56th ACM Symposium on Theory of Computing, STOC 2024. [arXiv]

• Radical Sylvester-Gallai Theorem for Tuples of Quadratics, 

with Abhibhav Garg, Rafael Oliveira and Shir Peleg,

 Computational Complexity Conference, CCC 2023. [ECCC]

• Radical Sylvester-Gallai Theorem for Cubics, 

with Rafael Oliveira, 

63rd IEEE Symposium on Foundations of Computer Science , FOCS 2022. [ECCC]

• Robust Radical Sylvester-Gallai Theorem for Quadratics, 

with Abhibhav Garg and Rafael Oliveira, 

Proc. of 38th International Symposium on Computational Geometry, SoCG 2022.  [arxiv]

• Geometric Consistency of Manin's Conjecture, 

with Brian Lehmann and Sho Tanimoto, 

Compositio Math.158 (2022), 1375-1427. [arxiv]

• Manin's Conjecture and the Fujita Invariant of Finite Covers, 

Algebra &  Number Theory, 15 (2021), 2071-2087. [arxiv]

• Manin's b-constant in Families, 

Algebra & Number Theory, 13  (2019), 1893-1905. [arxiv]

• Counterexamples to Mercat's Conjecture, 

Archiv der  Mathematik, 106  (2016), 439-444. [arxiv]