
Preprints:
(mostly preliminary versions)
Papers:
(the files below might be slightly different from the published versions)
2017 and papers to appear
 An example related to the slicing
inequality for general measures  joint with A. Koldobsky. To
appear in J. Funct. Anal.
 Optimal compression of approximate inner products and dimension
reduction  joint with N. Alon. To appear in FOCS 2017. Here
are related slides.
 Needle decompositions in Riemannian geometry.
Mem. Amer. Math. Soc., Vol. 249, No. 1180, (2017). Here are related slides.
 Remarks on curvature in the transportation metric  joint with A. V. Kolesnikov.
Analysis Math., Vol. 43, No. 1, (2017), 67–88.
 Convex geometry and waist inequalities.
Geometric and Functional Analysis (GAFA), Vol. 27, No. 1, (2017),
130–164.
 SuperGaussian directions of random
vectors. Geometric Aspects of Functional Analysis, Lecture Notes in
Math. 2169, Springer (2017), 187211. Here are related slides.
 Affine hemispheres of elliptic type.
To appear in Algebra i Analiz (St. Petersburg Math. Journal). Here
is an STL
file for 3Dprinting an affine
hemisphere
with a square base, courtesy of Quentin Merigot and Filippo Santambrogio.
 Eldan's stochastic
localization and
tubular neighborhoods of complexanalytic sets. To appear in
the Journal of Geometric Analysis.
2016
2015
2014:
 Logarithmicallyconcave moment measures I.
Geometric Aspects of Functional Analysis, Lecture Notes in Math. 2116, Springer (2014), 231260.
 On the oscillation rigidity of a Lipschitz function on a highdimensional flat torus
 joint with D. Faifman and V. D. Milman. Geometric Aspects of Functional Analysis, Lecture Notes in Math. 2116, Springer (2014), 123131.
 Concentration of measures supported on the cube. Israel J. of Math.,
Vol. 203, Issue 1, (2014), 5980.
 Dimensionality and the stability of the
BrunnMinkowski inequality  joint with
R. Eldan.
Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), Vol. XIII, (2014), 9751007.
2013:
2012:
 Inner regularization of logconcave measures and smallball estimates  joint with E. Milman.
Geometric Aspects of Functional Analysis, Lecture Notes in Math. 2050, Springer (2012), 267278.
 Interpolations, convexity and geometric inequalities  joint with D. CorderoErausquin. Geometric Aspects of Functional Analysis, Lecture Notes in Math. 2050, Springer (2012), 151168.
 Functional affineisoperimetry and an inverse logarithmic Sobolev inequality  joint with
S. ArtsteinAvidan, C. Schütt and E. Werner. J. Functional Analysis, Vol. 262, No. 9,
(2012), 41814204.
 Centroid bodies and the logarithmic Laplace transform  a unified approach  joint with E. Milman. J. Functional Analysis, Vol. 262, No. 1, (2012), 1034.
2011:
 Variations on the BerryEsseen theorem  joint with S. Sodin. Theory Probab. Appl. (also known as "Teoriya Veroyatnostei i ee Primeneniya"), Vol. 56, No. 3, (2011), 514533.
 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), 5568. Here are related slides.
 Quantum OneWay 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), 3140. Here are related slides.
2010:
2009:
 An example related to Whitney extension with almost minimal C^m norm  joint with C. Fefferman, Rev. Mat. Iberoamericana, 25, no. 2, (2009), 423446.
 Economical toric spines via Cheeger's Inequality  joint with N. Alon. Journal of Topology and Analysis, vol. 1, (2009), 101111.
 A BerryEsseen 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), 253268.
 Fitting a C^mSmooth Function to Data I  joint with C. Fefferman, Ann. of Math., 169, no. 1, (2009), 315346.
 Fitting a C^mSmooth Function to Data II  joint with C. Fefferman, Rev. Mat. Iberoamericana, 25, no. 1, (2009), 49273.
2008:
2007:
 Uniform almost subgaussian estimates for linear functionals on convex sets, Algebra i Analiz (St. Petersburg Math. Journal), Vol. 19, no. 1 (2007), 109148.
 A central limit theorem for convex sets, Invent. Math., Vol. 168, (2007), 91131.
 Powerlaw estimates for the central limit theorem for convex sets, J. Functional Analysis, Vol. 245, (2007), 284310.
 Marginals of geometric inequalities, Geometric Aspects of Functional Analysis, Lecture Notes in Math. 1910, Springer (2007), 133166.
 C^1 extensions of functions and stabilization of Glaeser refinements  joint with N. Zobin. Rev. Mat. Iberoamericana, Vol. 23, no. 2 (2007), 635669.
 Small ball probability and Dvoretzky Theorem  joint with R. Vershynin, Israel J. Math., Vol. 157, no. 1 (2007), 193207.
2006:
 Isomorphic and almostisometric problems in highdimensional convex geometry, proceedings of the Internat. Congress of Mathematicians, Madrid, Spain, 2006. Eurpoean Math. Soc., Vol. II, (2006), 15471562.
 On convex perturbations with a bounded isotropic constant, Geometric and Functional Analysis (GAFA), Vol. 16, Issue 6 (2006) 12741290.
2005:
2004:
 The Santalo point of a function, and a functional form of Santalo inequality  joint with S. Artstein, V. Milman, Mathematika 51 (2004) 3348.
 Rate of convergence of geometric symmetrization, Geometric and Functional Analysis (GAFA), Vol 14, Issue 6 (2004) 13221338.
 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) 101116.
 On Johntype ellipsoids, Geometric Aspects of Functional Analysis, Lecture Notes in Math. 1850, Springer (2004) 149158.
 A geometric inequality and a low Mestimate, Proc. Amer. Math. Soc., Vol. 132, No. 9, 29192628 (2004)
2003:
2002:
2000:
Ph.D. Thesis:

