Publications

Preprints:

(mostly preliminary versions)

Logarithmically-concave moment measures I. Preprint.
Moment measures - joint with D. Cordero-Erausquin. Preprint. Here are related slides.

(the files below might be slightly different from the published versions)

Concentration of measures supported on the cube. To appear in Israel J. of Math.
Dimensionality and the stability of the Brunn-Minkowski inequality - joint with R. Eldan. To appear in Ann. Sc. Norm. Super. Pisa.
Poincare inequalities and moment maps. Ann. Fac. Sci. Toulouse Math., Vol. 22, No. 1, (2013), 1--41. Here are related slides.

Inner regularization of log-concave measures and small-ball estimates - joint with E. Milman. Geometric Aspects of Functional Analysis, Lecture Notes in Math. 2050, Springer (2012), 267--278.
Interpolations, convexity and geometric inequalities - joint with D. Cordero-Erausquin. Geometric Aspects of Functional Analysis, Lecture Notes in Math. 2050, Springer (2012), 151--168.
Functional affine-isoperimetry and an inverse logarithmic Sobolev inequality - joint with S. Artstein-Avidan, C. Schütt and E. Werner. J. Funct. Anal., Vol. 262, No. 9, (2012), 4181--4204.
Centroid bodies and the logarithmic Laplace transform - a unified approach - joint with E. Milman. J. Funct. Anal., Vol. 262, No. 1, (2012), 10--34.

Variations on the Berry-Esseen theorem - joint with S. Sodin. Theory Probab. Appl. (also known as "Teoriya Veroyatnostei i ee Primeneniya"), Vol. 56, No. 3, (2011), 514--533.
Approximately gaussian marginals and the hyperplane conjecture - joint with R. Eldan. Proc. of a workshop on "Concentration, Functional Inequalities and Isoperimetry", Contermporary Mathematics 545, Amer. Math. Soc., (2011), 55--68. Here are related slides.
Quantum One-Way Communication is Exponentially Stronger Than Classical Communication - joint with O. Regev. STOC 2011 (Proceedings of a Symposium on Theory of Computing), Assoc. Comput. Mach., (2011), 31--40. Here are related slides.

On nearly radial marginals of high-dimensional probability measures. J. Eur. Math. Soc, Vol. 12, (2010), 723–-754. Here are related slides.
High-dimensional distributions with convexity properties. Proc. of the Fifth Euro. Congress of Math., Amsterdam, July 2008. Eur. Math. Soc. publishing house, (2010), 401--417. Here are related slides.

An example related to Whitney extension with almost minimal C^m norm - joint with C. Fefferman, Rev. Mat. Iberoamericana, 25, no. 2, (2009), 423--446.
Economical toric spines via Cheeger's Inequality - joint with N. Alon. Journal of Topology and Analysis, vol. 1, (2009), 101--111.
A Berry-Esseen type inequality for convex bodies with an unconditional basis. Probab. Theory Related Fields, vol. 45, no. 1, (2009), 1 -- 33.
On the hyperplane conjecture for random convex sets - joint with G. Kozma. Israel journal of math., vol. 170, no. 1, (2009), 253--268.
Fitting a C^m-Smooth Function to Data I - joint with C. Fefferman, Ann. of Math., 169, no. 1, (2009), 315--346.
Fitting a C^m-Smooth Function to Data II - joint with C. Fefferman, Rev. Mat. Iberoamericana, 25, no. 1, (2009), 49--273.

Pointwise Estimates for Marginals of Convex Bodies - joint with R. Eldan, J. Funct. Anal., Vol. 254, Issue 8, (2008), 2275--2293.
On volume distribution in 2-convex bodies - joint with E. Milman. Israel J. Math., Vol. 164 (2008), 221--249.

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.
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.
Marginals of geometric inequalities, Geometric Aspects of Functional Analysis, Lecture Notes in Math. 1910, Springer (2007), 133-166.
C^1 extensions of functions and stabilization of Glaeser refinements - joint with N. Zobin. Rev. Mat. Iberoamericana, Vol. 23, no. 2 (2007), 635--669.
Small ball probability and Dvoretzky Theorem - joint with R. Vershynin, Israel J. Math., Vol. 157, no. 1 (2007), 193--207.

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.
On convex perturbations with a bounded isotropic constant, Geom. and Funct. Anal. (GAFA), Vol. 16, Issue 6 (2006) 1274--1290.

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.

The Santalo point of a function, and a functional form of Santalo inequality - joint with S. Artstein, V. Milman, Mathematika 51 (2004) 33--48.
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.

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.