Area of research
Applied Mathematics · Geometry and Topology
Research interest
Research interests include Advanced Harmonic Analysis Research, Geometric and Algebraic Topology, Mathematical Analysis and Transform Methods, and Geometric Analysis and Curvature Flows.
Sharp Szemerédi-Trotter Constructions in the Plane
Degrees of maps and multiscale geometry
Systolic almost-rigidity modulo 2
Decoupling estimates in Fourier analysis
Macroscopic scalar curvature and codimension 2 width
Macroscopic scalar curvature and codimension 2 width
A sharp square function estimate for the cone in $\mathbb{R}^3$
On Falconer’s distance set problem in the plane
On Falconer's distance set problem in the plane
A sharp Schrödinger maximal estimate in $\mathbb{R}^2$
Strichartz estimates for the Schrödinger equation on irrational tori
2-Complexes with Large 2-Girth
Proof of the main conjecture in Vinogradov's Mean Value Theorem \break for degrees higher than three
Polynomial Methods in Combinatorics
Proof of the main conjecture in Vinogradov's mean value theorem for degrees higher than three
Polynomial partitioning for a set of varieties
A restriction estimate using polynomial partitioning
2-complexes with large 2-girth
On the Erdős distinct distances problem in the plane
A short proof of the multilinear Kakeya inequality
Distinct Distance Estimates and Low Degree Polynomial Partitioning
Unexpected Applications of Polynomials in Combinatorics