Field of Research:

Papers:

• A Berry-Esseen type inequality for convex bodies with an unconditional basis. To appear in Probab. Theory Related Fields.
• An example related to Whitney extension with almost minimal C^m norm - joint with C. Fefferman. To appear in Rev. Mat. Iberoamericana.
• On the hyperplane conjecture for random convex sets - joint with G. Kozma. To appear in Israel journal of math..
• A central limit theorem for convex sets, Invent. Math., Vol. 168, (2007), 91--131.
• Power-law estimates for the central limit theorem for convex sets, J. Funct. Anal., Vol. 245, (2007), 284--310.
• Pointwise Estimates for Marginals of Convex Bodies - joint with R. Eldan, J. Funct. Anal., Vol. 254, Issue 8, (2008), 2275--2293.
• Fitting a C^m-Smooth Function to Data I - joint with C. Fefferman, to appear in Ann. of Math.
• Fitting a C^m-Smooth Function to Data II - joint with C. Fefferman, to appear in Rev. Mat. Iberoamericana.
• Isomorphic and almost-isometric problems in high-dimensional convex geometry, proceedings of the Internat. Congress of Mathematicians, Madrid, Spain, 2006. Eurpoean Math. Soc., Vol. II, (2006), 1547--1562.
• Uniform almost sub-gaussian estimates for linear functionals on convex sets, Algebra i Analiz (St. Petersburg Math. Journal), Vol. 19, no. 1 (2007), 109--148.
• On convex perturbations with a bounded isotropic constant, Geom. and Funct. Anal. (GAFA), Vol. 16, Issue 6 (2006) 1274--1290.
• Marginals of geometric inequalities, Geometric Aspects of Functional Analysis, Lecture Notes in Math. 1910, Springer (2007), 133-166.
• On volume distribution in 2-convex bodies - joint with E. Milman. Israel J. Math., Vol. 164 (2008), 221--249.
• C^1 extensions of functions and stabilization of Glaeser refinements - joint with N. Zobin. Rev. Mat. Iberoamericana, Vol. 23, no. 2 (2007), 635--669.
• The Santalo point of a function, and a functional form of Santalo inequality - joint with S. Artstein, V. Milman, Mathematika 51 (2004) 33--48.
• Small ball probability and Dvoretzky Theorem - joint with R. Vershynin, Israel J. Math., Vol. 157, no. 1 (2007), 193--207.
• Geometry of log-concave functions and measures - joint with V. Milman, Geom. Dedicata 112 (2005) 169--182.
• An isomorphic version of the slicing problem, J. Funct. Anal. Vol. 218 (2005) 372 -- 394.
• Rapid Steiner symmetrization of most of a convex body and the slicing problem - joint with V. Milman. Combin. Probab. Comput. 14, no. 5-6 (2005) 829--843.
• Empirical processes and random projections - joint with S. Mendelson, J. Funct. Anal. 225, no. 1 (2005) 229--245.
• Rate of convergence of geometric symmetrization, Geom. and Funct. Anal. (GAFA), Vol 14, Issue 6 (2004) 1322--1338.
• Symmetrization and isotropic constants of convex bodies - joint with J. Bourgain, V. Milman. Geometric Aspects of Functional Analysis, Lecture Notes in Math. 1850, Springer (2004) 101-116.
• On John-type ellipsoids, Geometric Aspects of Functional Analysis, Lecture Notes in Math. 1850, Springer (2004) 149-158.
• A geometric inequality and a low M-estimate, Proc. Amer. Math. Soc., Vol. 132, No. 9, 2919-2628 (2004)
• A reduction of the slicing problem to finite volume ratio bodies - joint with J. Bourgain, V. Milman. C. R. Math. Acad. Sci. Paris 336 (2003), no. 4, 331-334.
• Isomorphic Steiner symmetrization - joint with V. Milman. Invent. Math. 153 (2003), no. 3, 463--485.
• 5n Minkowski symmetrizations suffice to arrive at an approximate Euclidean ball, Ann. of Math. 156 (2002), no. 3, 947--960.
• Remarks on Minkowski symmetrizations, Geometric Aspects of Functional Analysis, Lecture Notes in Math. 1745, Springer (2000) 109--117.



• My PhD thesis (and its short Hebrew version), written under the supervision of Prof. Vitali Milman at Tel-Aviv University.

Preprints:

• Economical toric spines via Cheeger's Inequality, joint with N. Alon.
• High-dimensional distributions with convexity properties.

Links:

• Photos
• Green Course