CV. Background. PAPERS and PREPRINTS. Funding.
Background	My research is in the fields of Harmonic Analysis and Geometric Measure Theory, with connections to Applied Mathematics. One part of my research lies on the interface between Harmonic Analysis and Geometric Measure Theory. It focuses on the theory of Quantitative Rectifiability. The goal is a quantitative study sets or measures, in a metric space (such as Euclidean space). This study is done via multiscale analysis. A second part of my research lies on the interface between Applied Mathematics and Harmonic Analysis or Geometric Measure Theory. In many applications one is given a large data set, represented as a subset of a metric space. A standard example is a subset of a high dimensional Euclidean space. One seeks to faithfully represent a large portion of this data set as a subset of a low dimensional Euclidean space. I did my undergraduate studies at the Hebrew University in Jerusalem, Israel. In May 2005 I received my Ph.D. in mathematics from Yale University. It was done under the supervision of Professor Peter Jones. From Fall 2005 to Spring 2009 I was an NSF Postdoc/Hedrick Assistant Professor at the UCLA mathematics department (with the Analysis group). I have been an Assistant Professor at the Stony Brook mathematics department since the fall of 2009. I am supported by the NSF as well as a fellowship from the Alfred P. Sloan Foundation.
Papers and Preprints	A Carleson packing condition for metric differentials. (Joint with Jonas Azzam) arxiv (abstract/ps/pdf) Hard Sard: Quantitative Implicit Function and Extension Theorems for Lipschitz Maps. (Joint with Jonas Azzam) GAFA, accepted. arxiv (abstract/ps/pdf) How to take shortcuts in Euclidean space: making a given set into a short quasi-convex set. (Joint with Jonas Azzam) Proc. London Math. Soc., accepted. arxiv (abstract/ps/pdf) A doubling measure on R^d can charge a rectifiable curve. (Joint with John Garnett and Rowan Killip) Proc. Amer. Math. Soc. vol. 138 (2010), pages 1673-1679 arxiv (abstract/ps/pdf) Christina Sormani and Stefan Wenger wrote a paper titled `Weak Convergence and Cancellation'. It has an appendix written by Stefan Wenger and myself. Calculus of Variations and Partial Differential Equations: Volume 38, Issue 1 (2010) , Page 183. arxiv (abstract/ps/pdf) Universal Local Parametrizations via Heat Kernels and Eigenfunctions of the Laplacian. (Joint with Peter W. Jones and Mauro Maggioni) Ann. Acad. Sci. Fenn. Math. vol. 35 (2010), pages 131-174 arxiv (abstract/ps/pdf) Manifold parametrizations by eigenfunctions of the Laplacian and heat kernels. (Joint with Peter W. Jones and Mauro Maggioni) PNAS, vol. 105 no. 6 (2008), pages 1803-1808 here is a draft in pdf format (may contain some typos). (this is an announcement of the results, and outline of proofs, which appear in full in the paper above) Big-Pieces-of-Lipschitz-Images Implies a Sufficient Carleson Estimate in a Metric Space arxiv (abstract/ps/pdf) Bi-Lipschitz Decomposition of Lipschitz functions into a Metric space. Revista Matemática Iberoamericana, vol 25, no. 2. Pages 521-531. arxiv (abstract/ps/pdf) Ahlfors-Regular Curves In Metric Spaces. Ann. Acad. Sci. Fenn. Math. 32 (2007), 437-460. arxiv (abstract/ps/pdf). Analyst's Traveling Salesman Theorems. A Survey. In the tradition of Ahlfors-Bers, IV, Contemporary Math., vol. 432, pages 209-220, AMS pdf or dvi (similar to the final version). Subsets of Rectifiable curves in Hilbert Space-The Analyst's TSP. Journal d'Analyse Mathematique 103 (2007), 331-375. arxiv (abstract/ps/pdf) (This paper is essentially the same as my PhD thesis)
Funding	Current Alfred P. Sloan Foundation NSF DMS 1100008. Past NSF DMS 0965766. NSF DMS 0800837 (turned into NSF DMS 0965766 when I moved to Stony Brook) NSF DMS 0502747 (NSF Postdoc)

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