(the files below might be slightly different from the published versions)
2024 and preprints

Horocyclic BrunnMinkowski inequality  joint with R. Assouline. Adv. Math., Vol. 436:109381, (2024), 39 pp.

A weak version of the epsilonDvoretzky conjecture for normed spaces  joint with T. Novikov. To appear in Israel Journal of Math.
 Spectral monotonicity under Gaussian convolution  joint with E. Putterman. To appear in Ann. Fac. Sci. Toulouse Math.

The strong data processing inequality under the heat flow  joint with O. Ordentlich. Preprint.
2023

Local tail bounds for polynomials on the discrete cube  joint with S. Sodin. Geometric Aspects of Functional Analysis, Lecture Notes in Math. 2327, Springer (2023), 223230.

Long lines in subsets of large measure in high dimension  joint with D. Elboim. Probab. Theory Related Fields 187, no. 34, (2023), 657–695. Here are related slides and video.

Linear extension operators for Sobolev spaces on uniform trees  joint with C. Fefferman. Advanced Nonlinear Studies, vol. 23: 20220075, no. 1, (2023), 18 pp.

Logarithmic bounds for isoperimetry and slices of convex sets. Ars Inveniendi Analytica (2023), Paper No. 4, 17 pp.
2022
 The slicing problem by Bourgain  joint with V. Milman. Analysis at Large, Dedicated to the
Life and Work of Jean Bourgain, edited by A. Avila, M. Rassias and Y. Sinai, Springer, (2022), 203–232.
 Bourgain's slicing problem and KLS isoperimetry up to polylog  joint with J. Lehec. Geometric and Functional Analysis (GAFA), Vol. 32, Springer (2022), 1134–1159.
2021

Rigidity of Riemannian embeddings of discrete metric spaces  joint with M. Eilat. Invent.
Math., Vol. 226, (2021), 349—391. Here is a relevant video and a notebook. 
Discrete variants of BrunnMinkowski type inequalities  joint with D. Halikias and Boaz Slomka. Ann. Fac. Sci. Toulouse Math. (6), Vol. 30, no. 2, (2021), 267—279.
2020
 Complex Legendre duality  joint with B. Berndtsson, D. CorderoErausquin and Y. A. Rubinstein. American Journal of Math., Vol. 142, No. 1, (2020). Here are related slides.
 Complex interpolation of Rnorms, duality and foliations  joint with B. Berndtsson, D. CorderoErausquin and Y. A. Rubinstein. J. Euro. Math. Soc., Vol. 22, Issue 2, (2020), 477–505. Here are related slides.
 A coordinatefree proof of the finiteness principle for the Whitney extension problem  joint with J. Carruth, A. FreiPearson and A. Israel. Rev. Mat. Iberoam., Vol. 36, no. 7, (2020), 1917–1956. Here is a clarification of a misleading remark from this paper.
 Unimodal value distribution of Laplace eigenfunctions and a monotonicity formula. Geom. Dedicata, Vol. 208, (2020), 13–29.
 Chasing nested convex bodies nearly optimally  joint with S. Bubeck, Y.T. Lee, Y. Li, M. Sellke. Symposium on Discrete Algorithms (SODA 2020), 1496–1508. Here is a relevant video and a notebook.
 The lower bound for Koldobsky's slicing inequality via random rounding  joint with G. V. Livshyts. Geometric Aspects of Functional Analysis, Lecture Notes in Math. 2266, Springer (2020), 4363. [Erratum: Julian Haddad noted an inaccuracy in Section 4 of the published version. We fixed this issue, and the corrected paper is available here and on arXiv].
 Spectral gaps, symmetries and logconcave perturbations  joint with F. Barthe. Bull. Hellenic Math. Soc., Vol. 64 (2020), 1–31.
2019
 Poisson processes and a logconcave Bernstein theorem  joint with J. Lehec. Studia Math., Vol. 247, (2019), 85–107.
 Extremal KahlerEinstein metric for twodimensional convex bodies  joint with A. V. Kolesnikov. Journal of Geometric Analysis, Vol. 29, Issue 3, (2019), 2347–2373.
 One more proof of the AlexandrovFenchel inequality  joint with D. CorderoErausquin, Q. Merigot, F. Santambrogio. Comptes Rendus Mathematique, Volume 357, Issue 8, (2019), 676680. Here is a related video and a notebook.
2018
 Isotropic constants and Mahler volumes. Advances in Math., Vol. 330, (2018), 74–108. Here are lecture notes from the Oberwolfach reports.
 An example related to the slicing inequality for general measures  joint with A. Koldobsky. J. Funct. Analysis, Vol. 274, Issue 7, (2018), 2089–2112.
 Estimates for moments of general measures on convex bodies  joint with S. Bobkov and A. Koldobsky. Proc. Amer. Math. Soc., Vol. 146, No. 11, (2018), 4879–4888.
 Eldan's stochastic localization and tubular neighborhoods of complexanalytic sets. Journal of Geometric Analysis, Vol. 28, Issue 3, (2018), 2008–2027.
2017
 Optimal compression of approximate inner products and dimension reduction  joint with N. Alon. Symposium on Foundations of Computer Science (FOCS 2017), 639–650. Here are related slides and video.
 Needle decompositions in Riemannian geometry. Mem. Amer. Math. Soc., Vol. 249, No. 1180, (2017). Here are related slides and video.
 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. Geom. Funct. Anal. (GAFA), Vol. 27, No. 1, (2017), 130–164. Here is a related video.
 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. Algebra i Analiz (St. Petersburg Math. Journal), Vol. 29, Issue 1, (2017), 145–188. Here is an STL file for 3Dprinting an affine hemisphere with a square base, courtesy of Quentin Merigot and Filippo Santambrogio.
2016
 Discrete curvature and abelian groups  joint with G. Kozma, P. Ralli and P. Tetali. Canad. J. Math. Vol. 68, No. 3, (2016), 655–674.
 Lipschitz functions on the infinitedimensional torus  joint with D. Faifman. Commun. Contemp. Math., Vol. 18, No. 1 (2016), 1550029
2015
 Moment measures  joint with D. CorderoErausquin. J. Functional Analysis, Vol. 268, No. 12, (2015), 3834–3866. Here are related slides.
 Eigenvalue distribution of optimal transportation  joint with A. V. Kolesnikov. Analysis & PDE., Vol. 8, No. 1, (2015), 33–55. Here is a related video.
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
 Poincare inequalities and moment maps. Ann. Fac. Sci. Toulouse Math., Vol. 22, No. 1, (2013), 141. Here are related slides.
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. Here are related slides.
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
 On nearly radial marginals of highdimensional probability measures. J. Eur. Math. Soc, Vol. 12, (2010), 723–754. Here are related slides.
 Highdimensional distributions with convexity properties. Proc. of the Fifth Euro. Congress of Math., Amsterdam, July 2008. Eur. Math. Soc. publishing house, (2010), 401417. Here are related slides and a loosely related video.
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
 Pointwise Estimates for Marginals of Convex Bodies  joint with R. Eldan, J. Functional Analysis, Vol. 254, Issue 8, (2008), 22752293.
 On volume distribution in 2convex bodies  joint with E. Milman. Israel J. Math., Vol. 164 (2008), 221249.
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. (A neat proof of Lemma 4.9 using Pinsker's inequality can be found here).
 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
 Geometry of logconcave functions and measures  joint with V. Milman, Geom. Dedicata 112 (2005) 169182.
 An isomorphic version of the slicing problem, J. Functional Analysis, 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. 56 (2005) 829843. [Erratum: The proof of Proposition 2.2 is bogus, fortunately a fix was found by Vritsiou].
 Empirical processes and random projections  joint with S. Mendelson, J. Functional Analysis, Vol. 225, no. 1 (2005) 229245.
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
 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, 331334.
 Isomorphic Steiner symmetrization  joint with V. Milman. Invent. Math. 153 (2003), no. 3, 463485.
2002
 5n Minkowski symmetrizations suffice to arrive at an approximate Euclidean ball, Ann. of Math. 156 (2002), no. 3, 947960.
2000
 Remarks on Minkowski symmetrizations, Geometric Aspects of Functional Analysis, Lecture Notes in Math. 1745, Springer (2000) 109117.
Ph.D. Thesis:
My PhD thesis (and its short Hebrew version), written under the supervision of Prof. Vitali Milman at TelAviv University.