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Preprints:
(mostly preliminary versions)
Papers:
(the files below might be slightly different from the published versions)
2018 and papers to appear
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.
- 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.
- Super-Gaussian directions of random
vectors. Geometric Aspects of Functional Analysis, Lecture Notes in
Math. 2169, Springer (2017), 187--211. 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 3D-printing an affine
hemisphere
with a square base, courtesy of Quentin Merigot and Filippo Santambrogio.
2016
2015
2014:
- Logarithmically-concave moment measures I.
Geometric Aspects of Functional Analysis, Lecture Notes in Math. 2116, Springer (2014), 231--260.
- On the oscillation rigidity of a Lipschitz function on a high-dimensional flat torus
- joint with D. Faifman and V. D. Milman. Geometric Aspects of Functional Analysis, Lecture Notes in Math. 2116, Springer (2014), 123--131.
- Concentration of measures supported on the cube. Israel J. of Math.,
Vol. 203, Issue 1, (2014), 59--80.
- Dimensionality and the stability of the
Brunn-Minkowski inequality - joint with
R. Eldan.
Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), Vol. XIII, (2014), 975--1007.
2013:
2012:
- 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. Functional Analysis, Vol. 262, No. 9,
(2012), 4181--4204.
- Centroid bodies and the logarithmic Laplace transform - a unified approach - joint with E. Milman. J. Functional Analysis, Vol. 262, No. 1, (2012), 10--34.
2011:
- 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.
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), 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.
2008:
2007:
- 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. Functional Analysis, 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.
2006:
- 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, Geometric and Functional Analysis (GAFA), Vol. 16, Issue 6 (2006) 1274--1290.
2005:
2004:
- 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, Geometric and Functional Analysis (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)
2003:
2002:
2000:
Ph.D. Thesis:
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