# Joris Roos

Van Vleck Visiting Assistant Professor
Department of Mathematics
480 Lincoln Drive
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, preprints, theses

1. 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.
2. 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 arXiv:1906.05997, 2019, submitted.
3. 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.
4. A maximal function for families of Hilbert transforms along homogeneous curves (with S. Guo, A. Seeger, P.-L. Yung)
Abstract pdf arXiv arXiv:1902.00096, 2019, submitted.
5. Averages of simplex Hilbert transforms (with P. Durcik)
Abstract pdf arXiv arXiv:1812.11701, 2018, submitted.
6. 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
7. Bounds for anisotropic Carleson operators
Abstract pdf arXiv Journal arXiv:1710.10962, 2017, J. Fourier Anal. Appl.
8. 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.
9. 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.
10. 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.
11. Singular integrals and maximal operators related to Carleson's theorem and curves in the plane
Abstract pdf ULB Doctoral dissertation, University of Bonn, 2017.
12. 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