Joris Roos is an Assistant Professor in the Mathematical Sciences Department at UMass Lowell.

Joris Roos

Assistant Professor

College
College of Sciences
Department
Mathematics and Statistics
Office
Southwick Hall 350V
Email
joris_roos@uml.edu
Links

Expertise

Fourier analysis, real analysis, computer-assisted proofs

Research Interests

  • 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

Education

  • Doctor of Philosophy (Ph.D.): Mathematics, University of Bonn, (2017)

Selected Publications

  • 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’s theorem. With S. Guo, P.-L. Yung. Analysis&PDE 13, no. 5, 1457-1500, 2020.

Selected Contracts, Fellowships, Grants and Sponsored Research

  • 2022-2025: National Science Foundation Grant DMS-2154835 “Topics in Harmonic Analysis: Maximal Functions, Singular Integrals, and Multilinear Inequalities”
  • 2021-2022: Simons Foundation Grant ID 855692 ”Topics in real and discrete harmonic analysis”
  • 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 ”Bellman functions and Poincar´e inequalities on the hypercube” (with P. Durcik, I. Holmes, P. Ivanisvili, A. Volberg)
  • 2018-2023 American Institute of Mathematics SQuaRE ”Geometric perspectives in harmonic analysis” (with P. Gressman, S. Guo, L. B. Pierce, P.-L. Yung)