I am broadly interested in harmonic analysis, probability theory and their interactions. In particular, I have primarily focused on sparse domination and weighted inequalities in non-homogeneous settings and in abstract probability spaces. Moreover, I have worked on martingale inequalities in absence of differential subordination and connections to harmonic analysis in presence of reflection symmetries. More recent interests involve Geometric Measure Theory and Boolean Harmonic Analysis.
Below is a list of my publications and preprints. Click on any title to view the paper on arXiv.
Matrix Weighted L^p Estimates in the Nonhomogeneous Setting. with F. Benito de la Cigoña, T. Borges, M. Pasquariello, and N. A. Wagner; Advances in Mathematics, Volume 492, 2026.
Optimal Sparse Bounds and Commutator Characterizations Without Doubling. with Y. Lin, N.A. Wagner, and B.D. Wick.
Martingale Transforms and Compensated Bellman Estimates for Dunkl Riesz Transforms. with B.D. Wick.
Predictable subordination, sharp martingale inequalities and applications.
An archive of the reading groups hosted by our research group at WashU in recent years. These meetings were dedicated to a deep study of specific areas within Harmonic Analysis, ranging from classical theory to modern applications.
Geometric Measure Theory - Spring 2026
We will explore the interplay between harmonic analysis and geometric measure theory, with a specific focus on how Fourier transform techniques are applied to problems involving Hausdorff dimension, fractals, and Falconer's distance set conjecture.
Reference: Mattila, Pertti. Fourier Analysis and Hausdorff Dimension
Bounded Analytic Functions - Fall 2025
This reading group is dedicated to the study of analytic function theory on the unit disk and upper half plane, with a specific emphasis on the interplay between complex analysis and real-variable harmonic analysis.
Reference: Garnett, John B. Bounded Analytic Functions
Almost Everywhere Convergence of Fourier Series - Fall 2025
We studied the celebrated Carleson's Theorem on almost everywhere convergence of Fourier series. The failure of classical Calderón-Zygmund theory to handle modulation-invariant operators necessitated the creation of new time-frequency techniques. This development also provided a robust framework for multilinear singular integrals, effectively solving the long-standing problem of the Bilinear Hilbert Transform.
Reference: Terence Tao's Lecture notes
Restriction Theory and Decoupling - Spring 2025
The restriction conjecture is a central problem in harmonic analysis about how the Fourier transform of an L^p function behaves when restricted to curved hypersurfaces. Several techniques that first emerged in the restriction theory, such as wave packet decompositions, rescaling, and bilinear or multilinear reductions, turned out to also be well suited to proving decoupling estimates. We focused on the Bourgain-Demeter Decoupling Theorem for the parabola.
Reference: Terence Tao's Lecture notes
Discrete Harmonic Analysis - Spring 2024
Modern topics at the interface of harmonic analysis, ergodic theory, number theory, and additive combinatorics. The main ideas were pioneered by Bourgain and Stein, motivated by questions involving averages over polynomial sequences, but the subject has grown significantly over the last 30 years and has steadily become one of the most dynamic areas of modern harmonic analysis.
Reference: Krause, Ben. Discrete Analogues in Harmonic Analysis: Bourgain, Stein, and Beyond.