Research Interest

I am interested in real algebraic geometry, convex geometric analysis and combinatorial geometry, and particularly excited to see interaction between these fields.

Current Topics of Study

Efficient real root finding, random real polynomials, sums of squares methods for optimization, tropical geometry, hyperbolic polynomials,
algebraic methods in combinatorial geometry

Writings

Tropical Varieties for Exponential Sums and Their Distance to Amoeba (with J.M Rojas and G. Paouris)
arxiv

Multihomogenous Nonnegative Polynomials and Sums of Squares arxiv

Probabilistic Condition Number Estimates for Real Polynomials I: A Broader Family of Distributions

(with J. M Rojas and G. Paouris) arxiv

Approximating Nonnegative Polynomials via Spectral Sparsification arxiv

In Preperation

Probabilistic Condition Number Estimates for Real Polynomials II: Sparse Polynomials

(with J. M Rojas and G. Paouris)

Volume Inequalities for Convex Hull and Minskowski Sum of Orbits (with P. Valettas)