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
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Find me on arXiv.
29. A fractal local smoothing problem for the wave equation. With David Beltran, Alex Rutar, Andreas Seeger.
arXiv:2501.12805, submitted
28. Spherical maximal operators with fractal sets of dilations on radial functions. With David Beltran, Andreas Seeger.
arXiv:2412.09390, submitted
27. Sharp isoperimetric inequalities on the Hamming cube near the critical exponent. With Polona Durcik, Paata Ivanisvili.
arXiv:2407.12674, accompanying code, submitted
26. Bochner-Riesz means at the critical index: Weighted and sparse bounds. With David Beltran, Andreas Seeger.
arXiv:2309.13487, Oberwolfach Preprints 2023:16, Mathematische Annalen 391, p. 2337-2383, 2025.
(Companion paper: A Note on Endpoint Bochner-Riesz Estimates. Oberwolfach Preprints 2023:17)
25. Endpoint sparse domination for classes of multiplier transformations. With David Beltran, Andreas Seeger.
arXiv:2212.12437, Mathematische Zeitschrift 305, Article Number: 11, 2023.
24. A new type of superorthogonality. With Philip T. Gressman, Lillian B. Pierce, Po-Lam Yung.
arXiv:2212.08956, Proceedings of the American Mathematical Society 152, p. 665-675, 2024.
23. A new proof of an inequality of Bourgain. With Polona Durcik.
arXiv:2210.01326, Mathematical Research Letters 31, no. 4, p. 1047-1060, 2024.
22. Spherical maximal operators on Heisenberg groups: Restricted dilation sets. With Andreas Seeger, Rajula Srivastava.
arXiv:2208.02774, Studia Mathematica 273, 1-28, 2023.
21. Discrete analogues of maximally modulated singular integrals of Stein-Wainger type: Lp bounds for p>1. With Ben Krause.
arXiv:2107.14616, Journal of Functional Analysis 285, no. 10, 110123, 2023.
20. On the strict majorant property in arbitrary dimensions. With Philip T. Gressman, Shaoming Guo, Lillian B. Pierce, Po-Lam Yung.
arXiv:2106.12538, Quarterly Journal of Mathematics 74, no. 1, 139-161, 2023.
19. Lebesgue space estimates for spherical maximal functions on Heisenberg groups. With Andreas Seeger, Rajula Srivastava.
arXiv:2103.09734, International Mathematics Research Notices 2022, no. 24, 19222-19257, 2022.
18. A Holey Perspective on Venn Diagrams. With Anna N. Bartel, Kevin J. Lande, Karen B. Schloss. Cognitive Science 46, no. 1, e13073, 2022.
17. Pointwise convergence of certain continuous-time double ergodic averages. With Michael Christ, Polona Durcik, Vjekoslav Kovač.
arXiv:2011.06370, Ergodic Theory and Dynamical Systems 42, no. 7, 2270-2280, 2022.
16. Multi-scale sparse domination. With David Beltran, Andreas Seeger.
arXiv:2009.00227, Memoirs of the American Mathematical Society, Volume 298, Number 1491, 2024.
15. Trilinear smoothing inequalities and a variant of the triangular Hilbert transform. With Michael Christ, Polona Durcik.
arXiv:2008.10140, Advances in Mathematics 390, Paper No. 107863, 2021.
14. Spherical maximal functions and fractal dimensions of dilation sets. With Andreas Seeger.
arXiv:2004.00984, American Journal of Mathematics 145, no. 4, 1077-1110, 2023.
13. Decoupling for two quadratic forms in three variables: a complete characterization. With Shaoming Guo, Changkeun Oh, Po-Lam Yung, Pavel Zorin-Kranich.
arXiv:1912.03995, Revista Matemática Iberoamericana 39, no. 1, 283–306, 2023.
12. Sparse bounds for discrete singular Radon transforms. With Theresa C. Anderson, Bingyang Hu.
arXiv:1911.03006, Colloquium Mathematicum 165, no. 2, 199-217, 2021.
11. Lp→Lq bounds for spherical maximal operators. With Theresa C. Anderson, Kevin Hughes, Andreas Seeger.
arXiv:1909.05389, Mathematische Zeitschrift 297, no. 3-4, 1057-1074, 2021.
10. Discrete analogues of maximally modulated singular integrals of Stein-Wainger type. With Ben Krause.
arXiv:1907.00405, Journal of the European Mathematical Society 24, no. 9, 3183-3213, 2022.
9. Maximal functions associated with families of homogeneous curves: Lp bounds for p≤2. With Shaoming Guo, Andreas Seeger, Po-Lam Yung.
arXiv:1906.05997, Proceedings of the Edinburgh Mathematical Society 63, no. 2, 398-412, 2020.
8. Reversing a philosophy: from counting to square functions and decoupling. With Philip T. Gressman, Shaoming Guo, Lillian B. Pierce, Po-Lam Yung.
arXiv:1906.05877, Journal of Geometric Analysis 31, no. 7, 7075–7095, 2021, Elias M. Stein: In Memoriam.
7. A maximal function for families of Hilbert transforms along homogeneous curves. With Shaoming Guo, Andreas Seeger, Po-Lam Yung.
arXiv:1902.00096, Mathematische Annalen 377, no. 1-2, 69-114, 2020.
6. Averages of simplex Hilbert transforms. With Polona Durcik.
arXiv:1812.11701, Proceedings of the American Mathematical Society 149, no. 2, 633-647, 2021.
5. Sharp variation-norm estimates for oscillatory integrals related to Carleson's theorem. With Shaoming Guo, Po-Lam Yung.
arXiv:1710.10988, Analysis & PDE 13, no. 5, 1457-1500, 2020.
4. Bounds for anisotropic Carleson operators.
arXiv:1710.10962, Journal of Fourier Analysis and Applications 25, no. 5, 2324-2355, 2019.
3. A polynomial Roth theorem on the real line. With Polona Durcik, Shaoming Guo.
arXiv:1704.01546, Transactions of the American Mathematical Society 371, no. 10, 6973-6993, 2019.
2. Maximal operators and Hilbert transforms along variable non-flat homogeneous curves. With Shaoming Guo, Jonathan Hickman, Victor Lie.
arXiv:1610.05203, Proceedings of the London Mathematical Society 115, no. 1, 177-219, 2017.
1. Polynomial Carleson operators along monomial curves in the plane. With Shaoming Guo, Lillian B. Pierce, Po-Lam Yung.
arXiv:1605.05812. Journal of Geometric Analysis 27, no. 4, 2977-3012, 2017.
0. Singular integrals and maximal operators related to Carleson's theorem and curves in the plane, Doctoral dissertation, University of Bonn, 2017. Universitäts- und Landesbibliothek Bonn
-1. Inner-outer factorization of analytic matrix-valued functions, Master's thesis, University of Bonn, 2014. arXiv:2412.12172