Research interests

My research work is focused on algebraic-geometric approaches for solving problems that originate in number theory, algebraic complexity theory and combinatorics. More specifically, I am interested in birational geometry, the Minimal Model Program and applications to the study of rational points and rational curves on algebraic varieties. I am also interested interactions between algebraic geometry and complexity theory. In this direction, my research work is on the Polynomial Identity Testing (PIT) problem via Sylvester-Gallai Configurations in combinatorial geometry.

Papers

• Uniform Bounds on Product Sylvester-Gallai Configurations,

with Abhibhav Garg and Rafael Oliveira, 

in preparation.

• 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]