Welcome! I was formerly a J.L. Doob Research Assistant Professor in the mathematics deparment at the University of Illinois at Urbana-Champaign. I am currently doing math outside of academia. I completed my PhD in 2019 at Brown University, advised by Jill Pipher.  Here is a copy of my thesis. 

Broadly speaking my research involved harmonic analysis and related fields, including dispersive partial differential equations. 

I can be reached at: aabarron412@gmail.com

Papers and Preprints

1. Appendix in Maximal Estimates for the Weyl sums on T^d, by Changxing Miao, Jiye Yuan, and Tengfei Zhao, J. Funct. Anal., Vol 284, Issue 2, Januray 2023, 109747 (arXiv)

2.  An L^4 maximal estimate for quadratic Weyl sums, Int. Math. Res. Not., Volume 2022, Issue 22, November 2022, Pages 17305–17332, (arXiv)

3. Global endpoint Strichartz estimates for Schrodinger equations on the cylinder RxT, with Michael Christ and Benoit Pausader,  Nonlinear Analysis (Harmonic analysis, dispersive and wave equations collection) Volume 206, May 2021, 112172 (arXiv)

4. Fourier decay of fractal measures on hyperboloids, with M. Burak Erdogan and Terence Harris,  Trans. Amer. Math. Soc. 374 (2021), 1041-1075  (arXiv)

5. Restriction estimates for hyperboloids in higher dimensions via bilinear estimates, Rev. Mat. Iberoam. 38 (2022), no. 5, 1453–1471  (arXiv)

6. On global-in-time Strichartz estimates for the semiperiodic Schrodinger equation, Analysis & PDE 14-4 (2021), 1125--1152  ( arXiv )

7. Sparse domination and the strong maximal function, with Jose M. Conde Alonso, Yumeng Ou, and Guillermo Rey. Adv. Math. 345 (2019), 1-26. (arXiv) 

8. Weighted Estimates for Rough Bilinear Singular Integrals via Sparse Domination, New York J. Math. (2017), 779-811. (Journal link)

9.  Sparse Bounds for Bi-Parameter Operators Using Square Functions, with Jill Pipher, preprint 2017 (arXiv )