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

Joris Roos

Assistant Professor

College
College of Sciences
Department
Mathematical Science
Office
Southwick 303Q
Links
Website

Expertise

Real Harmonic Analysis

Research Interests

Fourier analysis & harmonic analysis on Euclidean spaces: oscillatory integrals, maximal functions, singular integrals

Applications of real harmonic analysis to combinatorics, number theory, dispersive PDE and ergodic theory

Education

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

Selected Publications

  • Guo, S., Roos, J., Seeger, A., Yung, P. (2020). A maximal function for families of Hilbert transforms along homogeneous curves. Math. Ann.,377 69-114.
  • Christ, M., Durcik, P., Roos, J. (2020). A triangular Hilbert transform with curvature. Preprint, arXiv:2008.10140.
  • Krause, B., Roos, J. (2020). Discrete analogues of maximally modulated singular integrals of Stein-Wainger type. Preprint, arXiv:1907.00405.
  • Guo, S., Roos, J., Seeger, A., Yung, P. (2020). Maximal functions associated with families of homogeneous curves: Lp bounds for p≤2. Proc. Edinburgh Math. Soc.,63(2) 398-412.
  • Beltran, D., Roos, J., Seeger, A. (2020). Multi-scale sparse domination. Preprint, arXiv:2009.00227.
  • Guo, S., Roos, J., Yung, P. (2020). Sharp variation-norm estimates for oscillatory integrals related to Carleson's theorem. Analysis & PDE,13(5) 1457-1500.
  • Roos, J., Seeger, A. (2020). Spherical maximal functions and fractal dimensions of dilation sets. Preprint, arXiv:2004.00984.
  • Anderson, T.C., Hughes, K., Roos, J., Seeger, A. (2019). Lp→Lq bounds for spherical maximal operators. Math. Z., to appear.
  • Anderson, T.C., Hu, B., Roos, J. (2019). Sparse bounds for discrete singular Radon transforms. Colloq. Math., to appear.
  • Durcik, P., Guo, S., Roos, J. (2019). A polynomial Roth theorem on the real line. Trans. Amer. Math. Soc.,371(10) 6973-6993.
  • Roos, J. (2019). Bounds for anisotropic Carleson operators. J. Fourier Anal. Appl.,25(5) 2324-2355.
  • Guo, S., Oh, C., Roos, J., Yung, P., Zorin-Kranich, P. (2019). Decoupling for two quadratic forms in three variables: a complete characterization. Preprint, arXiv:1912.03995.
  • Gressman, P.T., Guo, S., Pierce, L.B., Roos, J., Yung, P. (2019). Reversing a philosophy: from counting to square functions and decoupling. J. Geom. Anal., to appear.
  • Durcik, P., Roos, J. (2018). Averages of simplex Hilbert transforms. Proc. Amer. Math. Soc., to appear.
  • Guo, S., Hickman, J., Lie, V., Roos, J. (2017). Maximal operators and Hilbert transforms along variable non-flat homogeneous curves. Proc. London Math. Soc.,115(1) 177-219.
  • Guo, S., Pierce, L.B., Roos, J., Yung, P. (2017). Polynomial Carleson operators along monomial curves in the plane. J. Geom. Anal.,27(4) 2977-3012.