Department of Mathematics
Cambridge, MA 02139
Email: dmal AT MIT DOT edu
I am an NSF postdoctoral fellow working in the analysis group at MIT. My primary research area is harmonic analysis, and I am especially interested in studying detailed properties of the Fourier transform. I grew up in Los Angeles, CA and spent 8 years in Berkeley as an undergraduate and PhD student (under my advisor, Mike Christ). At MIT, I have focused on decoupling theory (studying properties of functions with specialized Fourier support, like on a parabola) with Larry Guth.
Sharp superlevel set estimates for small cap decouplings of the parabola (with L. Guth and Y. Fu, arxiv) 2021.
Decoupling inequalities for short generalized Dirichlet sequences (with L. Guth and Y. Fu, arxiv) 2021.
Improved decoupling for the parabola (with L. Guth and H. Wang, arxiv) 2020, to appear in JEMS.
Regularized Brascamp-Lieb inequalities and an application 2019, to appear in Quart. J. Math.
Special cases of power decay in multilinear oscillatory integrals (with D. Dong and D. Villano), 2019, to appear in Applicable Analysis.
A symmetrization inequality shorn of symmetry (with M. Christ), Trans. Amer. Math. Soc. 373 (2020), no. 8, 59976028.
A constrained optimization problem for the Fourier transform: Quantitative analysis J. Geom. Anal. 29 (2019), no. 2, 12591301.
A constrained optimization problem for the Fourier transform: Existence (arxiv) 2018.
Problems related to Brascamp-Lieb inequalities
Conference in Honor of Andreas Seeger, AMS Special Session at UW Madison, SUMIRFAS, 2019
A constrained optimization problem for the Fourier transform
Analysis seminar, 2018, Georgia Tech, UCLA/Caltech, Michigan State
A restricted extremization problem for the Fourier transform
Young Women in Harmonic Analysis and PDE, 2016, University of Bonn
Character Table Methods for Calculating Rank of Finite Groups
Young Mathematicians Conference, The Ohio State University, August 2013
An elementary proof of the Hasse-Weil theorem for hyperelliptic curves. after S. Stepanov
Decoupling and Polynomial Methods in Analysis, 2017, University of Bonn
Fourier series as geometric rough paths
Harmonic analysis seminar 2016, UC Berkeley
The partial sum process of orthogonal expansion as geometric rough process with Fourier series as an
example, an improvement of Menshov-Rademacher theorem, after T. Lyons and D. Yang
Paraproducts and Analysis of Rough Paths, 2016, University of Bonn
Existence of Extremals for a Fourier Restriction Inequality, after M. Christ and S. Shao
Student Harmonic Analysis and Differential Equations Seminar, UC Berkely, September 2015
Sharp Inequalities in Harmonic Analysis, University of Bonn, August 2015
Fall 2020: Recitation instructor 18.01
Fall 2019: Recitation instructor 18.01
Spring 2016: GSI Math 202B
Spring 2014: GSI Math 1B
Fall 2013: GSI Math 54
Spring 2013: GSI Math 16B
|dmal AT mit DOT edu|