Research

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.

Papers/Preprints

• Maximum Gaussian Perimeter of Convex Sets in the Plane, in preparation.
• A Fourier Approach to Levine's Hat Puzzle (with Omer Tamuz). pdf
• Sphere Valued Noise Stability and Quantum MAX-CUT Hardness, to appear, Annals of Probability. 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), IEEE Transactions on Information Theory, 70 (2024), no. 8, 5516-5532. 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,  to appear, Journal of Graph Theory. ps dvi pdf
• Tree/Endofunction Bijections and Concentration Inequalities, Electronic Journal of Combinatorics, 29 (2022), no. 2, 2-33. 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

Lecture Notes

• 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

Websites

• Cornell research page
• Orthogonal polynomials page

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