Research

My research interests include: Analysis, Metric Geometry, Probability, and Harmonic Analysis.

My research advisor is Professor Assaf Naor

Euclidean Partitions that Optimize an Ornstein-Uhlenbeck Quadratic Form, preprint. ps dvi pdf.
Solution of the Propeller Conjecture in R^3, (with Aukosh Jagannath and Assaf Naor), submitted. ps dvi pdf. An extended abstract appeared in STOC 2012.
Orthogonal Polynomials with Respect to Self-Similar Measures, (with Philip Owrutsky and Robert S. Strichartz), Experiment. Math. 20 (2011), no. 3, 238-259. pdf
Localized Eigenfunctions: Here You See Them, There You Don't, (with Robert S. Strichartz), Notices Amer. Math. Soc. 57 (2010), no. 5, 624-629. pdf
Homotopies of Eigenfunctions and the Spectrum of the Laplacian on the Sierpinski Carpet, (with Robert S. Strichartz), Fractals 18 (2010), no. 1, 1-34. pdf
Outer Approximation of the Spectrum of a Fractal Laplacian, (with Tyrus Berry and Robert S. Strichartz), Experiment. Math. 18 (2009), no.4, 449-480. pdf

(Non-math)

A hydrogel-based microfluidic device for the studies of directed cell migration, Shing-Yi Cheng, Steven Heilman, Max Wasserman, Shivaun Archer, Michael L. Shuler and Mingming Wu. Lab on a Chip, 7(763), 2007. pdf
A three-channel microfluidic device for generating static linear gradients and its application to the quantitative analysis of bacterial chemotaxis, Jinpian Diao, Lincoln Young, Sue Kim, Elizabeth A. Fogarty, Steven M. Heilman, Peng Zhou, Michael L. Shuler, Mingming Wu and Matthew P. DeLisa. Lab on a Chip, 6(381), 2006. pdf

The Propeller Conjecture in R^3, STOC 2012 Slides pdf
Maximal Function Estimates of Naor and Tao, 2012. pdf
Recent Work on the Propeller Conjecture: How to prove a sharp inequality, 2011. pdf
Lecture Notes on Dvoretzsky's Theorem, 2010. pdf
The Radon and Fourier Transforms: The Mathematics of X-Rays and CT-Scans, 2010. pdf
Hearing the Shape of a Drum: Recent Results, 2009. pdf

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