Me on Google Scholar and MathSciNet. Also, Mathematical Lineage (updted 2024. Produced by Geneagrapher). CV. (pdf file) Background. PAPERS and PREPRINTS. Funding.
Background	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 Peter Jones. From Fall 2005 to Spring 2009 I was an NSF Postdoc/Hedrick Assistant Professor at the UCLA mathematics department. In fall 2009 I started as an Assistant Professor at the Stony Brook mathematics department. I am supported by the NSF. In the past I was also supported by a fellowship from the Alfred P. Sloan Foundation. (See Funding).
Papers and Preprints	(Authors are always in alphabetical order.) Characterizing rectifiability via biLipschitz pieces of Lipschitz mappings on the space (Joint with Sean Li) arxiv Coarse and pointwise tangent fields. (Joint with Guy C. David and Sylvester Eriksson-Bique) Submitted. arxiv Factorization and piecewise affine approximation of bi-Lipschitz mappings on large sets. (Joint with Guy C. David and Matthew Romney) Submitted. arxiv Square packings and rectifiable doubling measures (Joint with Matthew Badger) Discrete Analysis, 2025. arxiv Uniformly rectifiable metric spaces: Lipschitz images, Bi-Lateral Weak Geometric Lemma and Corona Decompositions (Joint with David Bate and Matthew Hyde) Submitted. arxiv Iterating the Big-Pieces operator and larger sets (Joint with Jared Krandel) Bulletin of the London Mathematical Society, 54: 2151-2161. arxiv Lower bounds on mapping content and quantitative factorization through trees (Joint with Guy C. David) Journal of the London Mathematical Society, 106 (2022), no. 2, 1170-1188. arxiv Quantitative decompositions of Lipschitz mappings into metric spaces (Joint with Guy C. David) Transactions of the American Mathematical Society, 376 (2023), no. 8, 5521-5571. arxiv Zoom Talk by Guy C. David on this paper. A sharp necessary condition for rectifiable curves in metric spaces (Joint with Guy C. David) Revista Matematica Iberoamericana, 7 (2021), no. 3, 1007-1044 arxiv An Analyst's Traveling Salesman Theorem for sets of dimension larger than one (Joint with Jonas Azzam) Mathematische Annalen, 370(3), 1389-1476 (2018). https://doi.org/10.1007/s00208-017-1609-0 Link arxiv The Analyst's traveling salesman theorem in graph inverse limits (Joint with Guy C. David) Ann. Acad. Sci. Fenn. Math. 42 (2017), 649-692. arxiv Multiscale analysis of 1-rectifiable measures II: characterizations (Joint with Matthew Badger) Anal. Geom. Metr. Spaces. Volume 5, Issue 1 (Mar 2017). arxiv Two sufficient conditions for rectifiable measures. (Joint with Matthew Badger) Proc. Amer. Math. Soc. 144 (2016), 2445-2454 arxiv An upper bound for the length of a Traveling Salesman path in the Heisenberg group. (Joint with Sean Li) Rev. Mat. Iberoam. 32 (2016), no. 2, 391-417. arxiv Multiscale analysis of 1-rectifiable measures: necessary conditions. (Joint with Matthew Badger) Mathematische Annalen: Volume 361, Issue 3 (2015), Page 1055-1072 arxiv The traveling salesman problem in the Heisenberg group: upper curvature bound. (Joint with Sean Li) Trans. of the Amer. Math. Soc. Volume 368, Number 7, July 2016, Pages 4585-4620 arxiv A quantitative metric differentiation theorem. (Joint with Jonas Azzam) Proc. Amer. Math. Soc. vol. 142 (2014), pages 1351-1357. arxiv Hard Sard: Quantitative Implicit Function and Extension Theorems for Lipschitz Maps. (Joint with Jonas Azzam) Geometric and Functional Analysis: Volume 22, Issue 5 (2012), Page 1062-1123. arxiv 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. (2012) 105 (2): 367-392. arxiv 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 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 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 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 Bi-Lipschitz Decomposition of Lipschitz functions into a Metric space. Revista Matemática Iberoamericana, vol 25, no. 2. Pages 521-531. arxiv Ahlfors-Regular Curves In Metric Spaces. Ann. Acad. Sci. Fenn. Math. 32 (2007), 437-460. arxiv. 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 (This paper is essentially the same as my PhD thesis)
Funding	Current NSF DMS 2154613 (2022 - 2025) Past NSF DMS 1763973 (2018 - 2022) NSF DMS 1361473 (2014 - 2018) NSF DMS 1100008 (2011 - 2014) Alfred P. Sloan Foundation (2010) NSF DMS 0800837 and 0965766 (2008 - 2011). Note: 0800837 turned into 0965766 when I moved to Stony Brook. NSF DMS MSPRF 0502747 (aka nsf postdoc) (2005 - 2009) Other NSF DMS 1954590 Conference Grant, SCGP, March 2020 NSF DMS 1700209 Conference Grant, Korea, May 2017 (Peter Jones) Any opinions, findings, and conclusions or recommendations expressed here or in these papers are those of the author(s) and do not necessarily reflect the views of the National Science Foundation

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