Research

Research interests

Real and discrete harmonic analysis: multilinear operators, geometric maximal operators, oscillatory integrals.
Interactions with fractal geometry, combinatorics, ergodic theory, information theory, number theory, PDE.
Formalization in Lean (1, 2, 3, 4) and computer-assisted numerical verification.

My research has received funding from

National Science Foundation (DMS-2555784, DMS-2154835)
Simons Foundation
American Institute of Mathematics
Studienstiftung (German Academic Scholarship Foundation)

Selected papers

Spherical maximal functions and fractal dimensions of dilation sets With A. Seeger American Journal of Mathematics 145, no. 4, 1077-1110 (2023)	arXiv journal
Discrete analogues of maximally modulated singular integrals of Stein-Wainger type With B. Krause Journal of the European Mathematical Society 24, no. 9, 3183-3213 (2022)	arXiv journal
Multi-scale sparse domination With D. Beltran, A. Seeger Memoirs of the American Mathematical Society 298, no. 1491 (2024)	arXiv journal
Trilinear smoothing inequalities and a variant of the triangular Hilbert transform With M. Christ, P. Durcik Advances in Mathematics 390, 107863 (2021)	arXiv journal
Sharp variation-norm estimates for oscillatory integrals related to Carleson's theorem With S. Guo, P.-L. Yung Analysis & PDE 13, no. 5, 1457-1500 (2020)	arXiv journal

Most of my papers are available on arXiv.

Journal publications

32. Sharp isoperimetric inequalities on the Hamming cube II: The critical exponent With P. Durcik, P. Ivanisvili, X. Xie arXiv:2602.20462, submitted	arXiv	code
31. Power weight inequalities for spherical maximal functions With M. Fraccaroli, A. Seeger arXiv:2602.17613, to appear in Math. Z.	arXiv	Lean
30. Problems on spherical maximal functions With A. Seeger arXiv:2511.11283, to appear in Bull. Amer. Math. Soc.	arXiv
29. A fractal local smoothing problem for the wave equation With D. Beltran, A. Rutar, A. Seeger Bulletin of the London Mathematical Society 57 (2025), no. 12, 3667-3690	arXiv journal
28. Spherical maximal operators with fractal sets of dilations on radial functions With D. Beltran, A. Seeger Studia Mathematica 289 (2026), 1-32	arXiv journal
27. Sharp isoperimetric inequalities on the Hamming cube near the critical exponent With P. Durcik, P. Ivanisvili arXiv:2407.12674, submitted	arXiv	code
26. Bochner-Riesz means at the critical index: Weighted and sparse bounds With D. Beltran, A. Seeger Mathematische Annalen 391, 2337-2383 (2025)	arXiv journal OWP
25. Endpoint sparse domination for classes of multiplier transformations With D. Beltran, A. Seeger Mathematische Zeitschrift 305, no. 1, 11 (2023)	arXiv journal
24. A new type of superorthogonality With P. T. Gressman, L. B. Pierce, P.-L. Yung Proceedings of the American Mathematical Society 152, 665-675 (2024)	arXiv journal	Lean
23. A new proof of an inequality of Bourgain With P. Durcik Mathematical Research Letters 31, no. 4, 1047-1060 (2024)	arXiv journal
22. Spherical maximal operators on Heisenberg groups: Restricted dilation sets With A. Seeger, R. Srivastava Studia Mathematica 273, 1-28 (2023)	arXiv journal
21. Discrete analogues of maximally modulated singular integrals of Stein-Wainger type II With B. Krause Journal of Functional Analysis 285, no. 10, 110123 (2023)	arXiv journal
20. On the strict majorant property in arbitrary dimensions With P. T. Gressman, S. Guo, L. B. Pierce, P.-L. Yung Quarterly Journal of Mathematics 74, no. 1, 139-161 (2023)	arXiv journal
19. Lebesgue space estimates for spherical maximal functions on Heisenberg groups With A. Seeger, R. Srivastava International Mathematics Research Notices 2022, no. 24, 19222-19257	arXiv journal
18. Pointwise convergence of certain continuous-time double ergodic averages With M. Christ, P. Durcik, V. Kovač Ergodic Theory and Dynamical Systems 42, no. 7, 2270-2280 (2022)	arXiv journal
17. Multi-scale sparse domination With D. Beltran, A. Seeger Memoirs of the American Mathematical Society 298, no. 1491 (2024)	arXiv journal
16. Trilinear smoothing inequalities and a variant of the triangular Hilbert transform With M. Christ, P. Durcik Advances in Mathematics 390, 107863 (2021)	arXiv journal
15. A Holey Perspective on Venn Diagrams With A. N. Bartel, K. J. Lande, K. B. Schloss Cognitive Science 46, no. 1, e13073 (2022)	journal
14. Spherical maximal functions and fractal dimensions of dilation sets With A. Seeger American Journal of Mathematics 145, no. 4, 1077-1110 (2023)	arXiv journal
13. Decoupling for two quadratic forms in three variables: a complete characterization With S. Guo, C. Oh, P.-L. Yung, P. Zorin-Kranich Revista Matemática Iberoamericana 39, no. 1, 283-306 (2023)	arXiv journal
12. Sparse bounds for discrete singular Radon transforms With T. C. Anderson, B. Hu Colloquium Mathematicum 165, 199-217 (2021)	arXiv journal
11. Lp to Lq bounds for spherical maximal operators With T. C. Anderson, K. Hughes, A. Seeger Mathematische Zeitschrift 297, 1057-1074 (2021)	arXiv journal
10. Discrete analogues of maximally modulated singular integrals of Stein-Wainger type With B. Krause Journal of the European Mathematical Society 24, no. 9, 3183-3213 (2022)	arXiv journal
9. Maximal functions associated with families of homogeneous curves: Lp bounds for p ≤<= 2 With S. Guo, A. Seeger, P.-L. Yung Proceedings of the Edinburgh Mathematical Society 63, no. 2, 398-412 (2020)	arXiv journal
8. Reversing a philosophy: from counting to square functions and decoupling With P. T. Gressman, S. Guo, L. B. Pierce, P.-L. Yung Journal of Geometric Analysis 31, 7075-7095 (2021)	arXiv journal
7. A maximal function for families of Hilbert transforms along homogeneous curves With S. Guo, A. Seeger, P.-L. Yung Mathematische Annalen 377, 69-114 (2020)	arXiv journal
6. Averages of simplex Hilbert transforms With P. Durcik Proceedings of the American Mathematical Society 149, 633-647 (2021)	arXiv journal
5. Sharp variation-norm estimates for oscillatory integrals related to Carleson's theorem With S. Guo, P.-L. Yung Analysis & PDE 13, no. 5, 1457-1500 (2020)	arXiv journal
4. Bounds for anisotropic Carleson operators Journal of Fourier Analysis and Applications 25, no. 5, 2324-2355 (2019)	arXiv journal
3. A polynomial Roth theorem on the real line With P. Durcik, S. Guo Transactions of the American Mathematical Society 371, 6973-6993 (2019)	arXiv journal
2. Maximal operators and Hilbert transforms along variable non-flat homogeneous curves With S. Guo, J. Hickman, V. Lie Proceedings of the London Mathematical Society 115, 177-219 (2017)	arXiv journal
1. Polynomial Carleson operators along monomial curves in the plane With S. Guo, L. B. Pierce, P.-L. Yung Journal of Geometric Analysis 27, no. 4, 2977-3012 (2017)	arXiv journal

Other publications, theses

A blueprint for the formalization of Carleson's theorem on convergence of Fourier series With L. Becker, M. I. de Frutos-Fernández, L. Diedering, F. van Doorn, S. Gouëzel, A. Jamneshan, E. Karunus, E. van de Meent, P. Monticone, J. Mulder-Sohn, J. Portegies, M. Rothgang, R. Srivastava, J. Sundstrom, J. Tan, C. Thiele arXiv:2405.06423v2, 2025	arXiv	Lean
A note on endpoint Bochner-Riesz estimates With D. Beltran, A. Seeger Oberwolfach Preprints 2023-17 (2023)	OWP
On the hole, interpretations of Venn diagrams are influenced by perceptual organization With A. N. Bartel, K. J. Lande, K. B. Schloss Journal of Vision 21, no. 9, 1989 (2021)	journal
Singular integrals and maximal operators related to Carleson's theorem and curves in the plane Ph.D. thesis, University of Bonn, 2017	ulb
Inner-outer factorization of analytic matrix-valued functions Master's thesis, University of Bonn, 2014	arXiv

Research

Research interests

Selected papers

Journal publications

Other publications, theses

Collaborators