My research interests include: Probability, Analysis, Geometry, Theoretical Computer Science.

My Ph.D. advisor was Professor Assaf Naor

Here is my thesis: ps dvi pdf.

*Ricci Curvature of Markov chains on the Discrete Square (with Georg Menz)*, in preparation.*Low Correlation Noise Stability of Euclidean Partitions*, in preparation.*The Structure of Gaussian Minimal Bubbles*, ps dvi pdf*A Periodic Isoperimetric Problem Related to the Unique Games Conjecture*, ps dvi pdf*Symmetric Convex Sets with Minimal Gaussian Surface Area*, ps dvi pdf*A Moment Majorization principle for random matrix ensembles with applications to hardness of the noncommutative Grothendieck problem*(with Thomas Vidick), ps dvi pdf*Low Correlation Noise Stability of Symmetric Sets*, ps dvi pdf*Strong Contraction and Influences in Tail Spaces*(with Elchanan Mossel and Krzysztof Oleszkiewicz), to appear, Transactions of the AMS. ps dvi pdf (video)*Standard Simplices and Pluralities are Not the Most Noise Stable*(with Elchanan Mossel and Joe Neeman), Israel Journal of Mathematics.**213**(2016), no. 1, 33-53. ps dvi pdf.*Euclidean Partitions Optimizing Noise Stability,*Electronic Journal of Probability.**19**(2014), no. 71, 1-37. ps dvi pdf.*Solution of the Propeller Conjecture in R^3,*(with Aukosh Jagannath and Assaf Naor), Discrete & Computational Geometry.**50**(2013), no. 2, 263-305. ps dvi pdf. An extended abstract appeared in STOC 2012. supporting code*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

*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

*Symmetric Convex Sets with Minimal Gaussian Surface Area.*2017. pdf*Noncommutative Majorization Principles and Grothendieck's Inequality.*2016. pdf*Low Correlation Noise Stability of Euclidean Sets.*2015. pdf*Real Analysis in Computer Science: A collection of Open problems.*with Yuval Filmus, Hamed Hatami, Elchanan Mossel, Ryan O'Donnell, Sushant Sachdeva, Andrew Wan, and Karl Wimmer. 2014. pdf*Strong Contraction and Influences in Tail Spaces*, 2014. pdf (video)*Standard Simplices and Pluralities for Unequal Measures are Not the Most Noise Stable*, 2014. pdf*Isoperimetry and the Ornstein-Uhlenbeck Operator*, 2013. pdf*The Propeller Conjecture in R^3*, STOC 2012 Slides. pdf (video: start at 1:45)*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