Joris Roos

Expertise

Fourier analysis, real analysis, computer-assisted proofs

Fourier analysis and harmonic analysis on Euclidean spaces: oscillatory integrals, maximal functions, singular integrals, discrete analogues
Applications of real harmonic analysis to combinatorics, number theory, dispersive PDE, ergodic theory and fractal geometry
Formalization of mathematics, computer-assisted proofs, interval arithmetic

Multi-scale sparse domination. With D. Beltran, A. Seeger. Memoirs of the American Mathematical Society, Volume 298, Number 1491, 2024.
Spherical maximal functions and fractal dimensions of dilation sets. With A. Seeger. American Journal of Mathematics 145, no. 4, 1077-1110, 2023.
Discrete analogues of maximally modulated singular integrals of Stein-Wainger type. With B. Krause. Journal of the European Mathematical Society 24, no. 9, pp. 3183-3213, 2022.
Trilinear smoothing inequalities and a variant of the triangular Hilbert transform. With M. Christ, P. Durcik. Advances in Mathematics 390, 107863 (40 pp.), 2021.
Sharp variation-norm estimates for oscillatory integrals related to Carleson鈥檚 theorem. With S. Guo, P.-L. Yung. Analysis&PDE 13, no. 5, 1457-1500, 2020.

2022-2025: National Science Foundation Grant DMS-2154835 鈥淭opics in Harmonic Analysis: Maximal Functions, Singular Integrals, and Multilinear Inequalities鈥�
2021-2022: Simons Foundation Grant ID 855692 鈥漈opics in real and discrete harmonic analysis鈥�
2021, 2022, 2024: Fellowships at Hausdorff Research Institute for Mathematics, Bonn
2023: Oberwolfach Research Fellowship, with D. Beltran and A. Seeger
2021-2025: American Institute of Mathematics SQuaRE 鈥滲ellman functions and Poincar麓e inequalities on the hypercube鈥� (with P. Durcik, I. Holmes, P. Ivanisvili, A. Volberg)
2018-2023 American Institute of Mathematics SQuaRE 鈥滸eometric perspectives in harmonic analysis鈥� (with P. Gressman, S. Guo, L. B. Pierce, P.-L. Yung)