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

- Fall 2019: CompSci/Math 514 - Numerical Analysis
- Fall 2019: Math 522 - Analysis II
- Spring 2019: Math 629 - Introduction to Measure and Integration
- Fall 2018: Math 522 - Analysis II
- Fall 2018: Math 921 - Graduate Seminar in Analysis
- Spring 2018: Math 421 - Theory of Single Variable Calculus
- Spring 2018: Math 522 - Analysis II
- Fall 2017: Math 522 - Analysis II

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

- 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

*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.*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.*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.*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.*Averages of simplex Hilbert transforms (with P. Durcik)*

Abstract pdf arXiv arXiv:1812.11701, 2018, submitted.*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*Bounds for anisotropic Carleson operators*

Abstract pdf arXiv Journal arXiv:1710.10962, 2017, J. Fourier Anal. Appl.*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.*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.*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.*Singular integrals and maximal operators related to Carleson's theorem and curves in the plane*

Abstract pdf ULB Doctoral dissertation, University of Bonn, 2017.*Inner-outer factorization of analytic matrix-valued functions*

Abstract pdf Master's thesis, University of Bonn, 2014.

Madison Lectures in Fourier Analysis 2019

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