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.

*Maximum Gaussian Perimeter of Convex Sets in the Plane*, in preparation.*Graph Neural Networks and Max-k-Cut*, in preparation.*Sphere Valued Noise Stability and Quantum MAX-CUT Hardness*. ps dvi pdf*Three Candidate Plurality is Stablest for Correlations at most 1/10*. ps dvi pdf*Hyperstable Sets with Voting and Algorithmic Hardness Applications*. ps dvi pdf*Noise Stability of Ranked Choice Voting*. ps dvi pdf*Convex Cylinders and the Symmetric Gaussian Isoperimetric Problem*. ps dvi pdf*Dimension-Free Noninteractive Simulation from Gaussian Sources*(with Alex Tarter). ps dvi pdf*A Variational Proof of Robust Gaussian Noise Stability*. ps dvi pdf (video)*Three Candidate Plurality is Stablest for Small Correlations*(with Alex Tarter), Forum of Mathematics Sigma.**9**(2021), E65. ps dvi pdf (video)*Independent Sets of Random Trees and of Sparse Random Graphs.*ps dvi pdf*Tree/Endofunction Bijections and Concentration Inequalities,*to appear, Electronic Journal of Combinatorics. ps dvi pdf*Designing Stable Elections*, a Survey, Notices of the AMS.**68**(2021), no. 4, 516–527. ps dvi pdf. A shorter news-style article, appeared in The Conversation, 16 July 2020. Discussed this work on the Data Skeptic podcast, 31 August, 2020*Stable Gaussian Minimal Bubbles*, to appear, Calculus of Variations and PDE. ps dvi pdf*The Structure of Gaussian Minimal Bubbles,*Journal of Geometric Analysis*.***31**(2021), no. 6, 6307–6348. ps dvi pdf*A Periodic Isoperimetric Problem Related to the Unique Games Conjecture*, Random Structures Algorithms.**56**(2020), no. 1, 154–168. ps dvi pdf*Symmetric Convex Sets with Minimal Gaussian Surface Area*, American Journal of Mathematics.**143**(2021), no. 1, 53–94. ps dvi pdf*A Moment Majorization principle for random matrix ensembles*. ps dvi pdf*Low Correlation Noise Stability of Symmetric Sets*, Journal of Theoretical Probability.**34**(2021), 2192–2240. ps dvi pdf*Strong Contraction and Influences in Tail Spaces*(with Elchanan Mossel and Krzysztof Oleszkiewicz), Transactions of the AMS.**369**(2017), no. 7, 4843–4863. 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

* (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

*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

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