Real and discrete harmonic analysis: multilinear singular integrals, maximal operators, oscillatory integrals
Interactions with related areas such as fractal geometry, combinatorics, ergodic theory, number theory and PDE
Proof assistants (Lean), computer-assisted numerical verification
My research has received funding from
Spherical maximal functions and fractal dimensions of dilation sets. With Andreas Seeger.
American Journal of Mathematics 145, no. 4, 1077-1110, 2023.
Discrete analogues of maximally modulated singular integrals of Stein-Wainger type. With Ben Krause.
Journal of the European Mathematical Society 24, no. 9, 3183-3213, 2022.
Multi-scale sparse domination. With David Beltran and Andreas Seeger.
Memoirs of the American Mathematical Society, Volume 298, Number 1491, 2024.
Trilinear smoothing inequalities and a variant of the triangular Hilbert transform. With Michael Christ and Polona Durcik.
Advances in Mathematics 390, Paper No. 107863, 2021.
Sharp variation-norm estimates for oscillatory integrals related to Carleson's theorem. With Shaoming Guo and Po-Lam Yung.
Analysis & PDE 13, no. 5, 1457-1500, 2020.
Most of my papers are available on arXiv.
Singular integrals and maximal operators related to Carleson's theorem and curves in the plane. University of Bonn, 2017. Universitäts- und Landesbibliothek Bonn