Alex Barron

Graduate Student
Brown University

Contact Info

Department of Mathematics
Box 1917
Brown University
151 Thayer Street
Providence, RI 02912

Office 016 (in Kassar House)

Email: abarron [at] math.brown.edu
            alexander_barrron [at] brown.edu

Research

I am a fifth-year graduate student in the mathematics department working with Jill Pipher. Here is my CV.

My research concerns the analysis of singular integral operators and oscillatory integrals that arise in harmonic analysis and related fields, along with applications to the study of partial differential equations. I am also interested in the intersection of harmonic analysis and probability theory, and in the various combinatorial methods that have been developed in conjunction with contemporary Fourier analysis (for example, the polynomial method).

Recently I have been studying global-in-time Strichartz estimates for dispersive equations on `wave-guides' (product manifolds with a Euclidean component and a torus component). A recent preprint is available here.

I am also interested in sparse bounds for various operators arising in harmonic analysis, in particular in the setting of multi-parameter operators. My work on sparse bounds can be found below. 


Papers and Preprints

1. (with J.M. Conde Alonso, Y. Ou, and G. Rey). Sparse domination and the strong maximal function, Adv. Math. 345 (2019), 1-26.  arxiv

2. On global-in-time Strichartz estimates for the semiperiodic Schrodinger equation, arxiv

3. (with J. Pipher) Sparse Bounds for Bi-Parameter Operators Using Square Functions,  arxiv

4. Weighted Estimates for Rough Bilinear Singular Integrals via Sparse Domination, New York Journal of Math. 23 (2017) 779- 811



Teaching

Spring 2018: Multi-variable Calculus, instructor

Fall 2017: Calculus 1, instructor

Spring 2017: Partial Differential Equations, TA

Fall 2016:  Calculus 1, instructor

Spring 2016: Multi-variable Calculus, TA

Fall 2015: Calculus 2,  TA

(all at Brown University)