Joris Roos

Van Vleck Visiting Assistant Professor
Department of Mathematics
University of Wisconsin-Madison
480 Lincoln Drive. Madison, WI-53706, USA
Office: VV 513
Email: jroos (at) math (dot) wisc (dot) edu



Teaching

August 2018: Student workshop on Automated Theorem Proving and Artificial Intelligence (Leysin, Switzerland)

Fall 2018: Reading Seminar on Vapnik-Chervonenkis dimension and the independence property

Research

Research interests

  • Real harmonic analysis, in particular multilinear singular integrals, oscillatory integrals, singular and maximal Radon transforms, variants of Carleson's theorem, time-frequency analysis, decoupling inequalities, discrete analogues
  • Connections of harmonic analysis to related fields such as combinatorics, number theory and dispersive PDE
  • Publications and preprints

    1. Spherical maximal functions and fractal dimensions of dilation sets (with A. Seeger)
      Abstract pdf arXiv arXiv:2004.00984, 2020, submitted.
    2. Decoupling for two quadratic forms in three variables: a complete characterization (with S. Guo, C. Oh, P.-L. Yung, P. Zorin-Kranich)
      Abstract pdf arXiv arXiv:1912.03995, 2019, submitted.
    3. Sparse bounds for discrete singular Radon transforms (with T. Anderson, B. Hu)
      Abstract pdf arXiv arXiv:1911.03006, 2019, submitted.
    4. $L^p\to L^q$ bounds for spherical maximal operators (with T. Anderson, K. Hughes, A. Seeger)
      Abstract pdf arXiv arXiv:1909.05389, 2019, to appear in Math. Z.
    5. Discrete analogues of maximally modulated singular integrals of Stein-Wainger type: $\ell^2(\mathbb{Z}^n)$ bounds
      Abstract pdf arXiv arXiv:1907.00405, 2019, submitted.
    6. Maximal functions associated with families of homogeneous curves: $L^p$ bounds for $p\le 2$ (with S. Guo, A. Seeger, P.-L. Yung)
      Abstract pdf arXiv Journal arXiv:1906.05997, Proc. Edinburgh Math. Soc. 63, no. 2, 398-412, 2020.
    7. Reversing a philosophy: from counting to square functions and decoupling (with P. T. Gressman, S. Guo, L. B. Pierce, P.-L. Yung)
      Abstract pdf arXiv arXiv:1906.05877, 2019, submitted.
    8. A maximal function for families of Hilbert transforms along homogeneous curves (with S. Guo, A. Seeger, P.-L. Yung)
      Abstract pdf arXiv Journal arXiv:1902.00096, Mathematische Annalen 377, 69-114, 2020.
    9. Averages of simplex Hilbert transforms (with P. Durcik)
      Abstract pdf arXiv arXiv:1812.11701, 2018, to appear in Proc. Amer. Math. Soc.
    10. Sharp variation-norm estimates for oscillatory integrals related to Carleson's theorem (with S. Guo, P.-L. Yung)
      Abstract pdf arXiv arXiv:1710.10988, 2017, to appear in Analysis&PDE
    11. Bounds for anisotropic Carleson operators
      Abstract pdf arXiv Journal arXiv:1710.10962, J. Fourier Anal. Appl. 25, no. 5, 2324-2355, 2019.
    12. A polynomial Roth theorem on the real line (with P. Durcik, S. Guo)
      Abstract pdf arXiv Journal arXiv:1704.01546, Trans. Amer. Math. Soc. 371, no. 10, 6973-6993, 2019.
    13. Maximal operators and Hilbert transforms along variable non-flat homogeneous curves (with S. Guo, J. Hickman, V. Lie)
      Abstract pdf arXiv Journal arXiv:1610.05203, Proc. London Math. Soc. 115, no. 1, 177-219, 2017.
    14. Polynomial Carleson operators along monomial curves in the plane (with S. Guo, L. B. Pierce, P.-L. Yung)
      Abstract pdf arXiv Journal arXiv:1605.05812, J. Geom. Anal. 27, no. 4, 2977-3012, 2017.

    Theses

    1. Singular integrals and maximal operators related to Carleson's theorem and curves in the plane
      Abstract pdf ULB Doctoral dissertation, University of Bonn, 2017.
    2. Inner-outer factorization of analytic matrix-valued functions
      Abstract pdf Master's thesis, University of Bonn, 2014.

    Local conferences

    Madison Lectures in Fourier Analysis 2019

    AMS Sectional Meeting in Madison, September 14-15, 2019