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.
- Stable Gaussian Minimal Bubbles. ps dvi pdf
- The Structure of Gaussian Minimal Bubbles. ps dvi pdf
- A Periodic Isoperimetric Problem Related to the Unique Games Conjecture, to appear, Random Structures and Algorithms. ps dvi pdf
- Symmetric Convex Sets with Minimal Gaussian Surface Area, to appear, American Journal of Mathematics. 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), 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
- 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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