Recent publications, Gideon Schechtman

• Lectures' slides

• GAFA seminar 1996 - 2000 (V.D. Milman and G. Schechtman, eds)
• GAFA seminar 2001 - 2002 (V.D. Milman and G. Schechtman, eds)
• GAFA seminar 2002 - 2003 (V.D. Milman and G. Schechtman, eds)
• GAFA seminar 2004 - 2005 (V.D. Milman and G. Schechtman, eds)

The versions of some of the papers below may be slightly different from the published ones.

• An ``isomorphic" version of Dvoretzky's theorem (with V.D. Milman), C. R. Acad. Sci. Paris t. 321 S\'erie I, (1995), 541--544.
• A remarkable rearrangement of the Haar system (with P.F.X. Muller), Proc. A.M.S. 125 (1997), 2363--2371.
• Banach spaces determined by their uniform structures (with W.B. Johnson and J. Lindenstrauss), Geometric and Funct. Anal. 6 (1996), 430--470.
• Hypercontractivity and comparison of moments of iterated maxima and minima of independent random variables (with P. Hitczenko, S. Kwapien, W. Li, Th. Schlumprecht and J. Zinn), Electronic J. of Prob. 3 (1998), paper no. 2, 1--26.
• On the Gaussian measure of the intersection of symmetric, convex sets (with Th. Schlumprecht and J. Zinn), Ann. Prob. 26 (1998), 346--357.
• Global vs. local asymptotic theories of finite dimensional normed spaces (with V.D. Milman), Duke Math. J. 90 (1997), 73--93.
• An ``isomorphic" version of Dvoretzky's theorem II (with V.D. Milman), Convex geometric analysis (Berkeley, CA, 1996), Math. Sci. Res. Inst. Publ., 34, Cambridge Univ. Press, Cambridge, (1999).
• Affine approximation of Lipschitz functions and nonlinear quotients (with S. Bates, W.B. Johnson, J. Lindenstrauss and D. Preiss), Geometric and Funct. Anal., 9 (1999), 1092--1127.
• Averages of norms and behavior of families of projective caps on the sphere (with A.E. Litvak and V.D. Milman), C. R. Acad. Sci. Paris t. 325 S\'erie I, (1997), 289--294.
• Averages of norms and quasi-norms (with A.E. Litvak and V.D. Milman), Math. Annalen 312 (1998), 95--124.
• Uniform quotient mappings of the plane (with W.B. Johnson, J. Lindenstrauss and D. Preiss), Michigan Math. J. 47 (2000), 15--31.
• Embedding subspaces of $L_p$ into $\ell^N_p$, $0<p<1$ (with A. Zvavitch), Math. Nachr. 227 (2001), 133--142.
• Concentration, results and applications, in preparation for handbook, preliminary version available.
• Finite dimensional subspaces of $L_p$ (with W.B. Johnson), Handbook of the Geometry of Banach Spaces, Vol 1, W.B. Johnson and J. Lindenstrauss, eds, Elsevier, Amsterdam (2001), 837--870.
• Upper bounds on the height difference of the Gaussian random field and the range of random graph homomorphism into Z (with I. Benjamini), Random Structures \& Algorithms 17 (2000), 20--25.
• Concentration on the $\ell_p^n$ ball (with J. Zinn), GAFA Seminar 1996-2000, Lecture Notes in Math., Vol. 1745, pp. 245--256, Springer (2000).
• An editorial comment on the preceding paper, GAFA Seminar 1996-2000, Lecture Notes in Math., Vol. 1745, pp. 19--20, Springer (2000).
• Almost Frechet differentiability of Lipschitz mappings between infinite dimensional Banach spaces (with W.B. Johnson, J. Lindenstrauss and D. Preiss), Proc. London Math. Soc., 84 (2002), 711--746.
• On Characterization of Two-Sample $U$-Statistic (with E. Schechtman), Statistics & Probability Letters, 58 (2002), 53--59.
• On the optimality of the random hyperplane rounding technique for MAX CUT (with U. Feige), Random Structures \& Algorithms, 20 (2002),  403--440.
• On the integrality ratio of semidefinite relaxations of MAX CUT, (with U. Feige, a short version of the paper above), Proceedings of the thirty-third annual ACM symposium on Theory of computing (2001), 433--442.
• Maximal $\ell_p^n$-structures in spaces with extremal parameters (with N. Tomczak-Jaegermann and R. Vershynin), GAFA Seminar 2001-2002, Lecture Notes in Math., Vol 1807,  (2003)
• Lipschitz quotients from metric trees and from Banach spaces containing $\ell_1$ (with W.B. Johnson, J. Lindenstrauss and D. Preiss), J. Funct. Anal, 194 (2002), 332—346.
• Block bases of the Haar system as complemented subspaces of $L_p$, $2<p<\infty$ (with D. Kleper), Proc. AMS, 131 (2003), 433--439.
• Remarks on Non Linear Type and Pisier's Inequality (with A. Naor), J. Reine Angew. Math. 552 (2002), 213-236.
• Vitur Yolid Vitur (in Hebrew), Haaretz, p. B2, March 5, 2002.  This is an editted version of Hazazat Ha'agala Ha'tkuah (in Hebrew MSWord).
• A characterization of relatively decomposable Banach lattices (with M. Cwikel and P.G. Nilsson), Memoir AMS, 787, 127 p. (2003).
• Very tight embeddings of subspaces of $L_p$, $1\le p<2$, into $\ell_p^n$ (with W.B. Johnson ), Geometric and Funct. Anal., 13 (2003), 845--851.
• Graphs with tiny vector chromatic numbers and huge chromatic numbers (with U. Feige and M. Langberg), SICOMP, volume 33, issue 6 , 1338--1368 (2004).
• The Shattering dimension of sets of linear functionals (with S. Mendelson), Ann. Prob., 32 (2004), 1746--1770.
• Special orthogonal splittings of $L_1^{2k}$, Israel J. Math. 139 (2004).
• Several remarks concerning the local theory of $L_p$ spaces (with W.B. Johnson), GAFA Seminar 2002-2003, 139--148, Lecture Notes in Math., Vol 1850, Springer-Verlag (2004).
• Two observations regarding embedding subsets of Euclidean spaces in normed spaces, Advances in Mathematics 200 (2006) 125--135.
• Weakly null sequences in $L_1$ (with W.B. Johnson and B. Maurey), Journal AMS, 20 (2007), 25-36.
• Complexity Measures of Sign Matrices (with N. Linial, S. Mendelson and A. Shraibman), Combinatorica 27 (2007), no. 4, 439--463.
• Planar earthmover is not in $L_1$ (with A. Naor), SIAM Journal on Computing, 37 Issue 3, 804-826 (2007) (short version in proceedings of FOCS 2006).
• The random version of Dvoretzky's theorem in $\ell_\infty^n$, GAFA Seminar 2004-2005, 265—270, Lecture Notes in Math., Vol 1910, Springer-Verlag (2007).
• The UGC hardness threshold of the Lp Grothendieck problem (with G. Kindler and A. Naor), Mathematics of Operations Research 35 (2010 ), 267-283 (extended abstract in SODA 2008).
• Extremal configurations for moments of sums of independent positive random variables, Banach Spaces and their Applications in Analysis, de Gruyter (2007).
• Non-linear factorization of linear operators (with W.B. Johnson and B. Maurey), Bull. Lond. Math. Soc. 41 (2009), no. 4, 663--668.
• Multiplication operators on $L(L_p)$ and $p$-strictly singular operators (with W.B. Johnson), J. Eur. Math. Soc. (JEMS) 10 (2008), no. 4, 1105--1119.
• Lower bounds for local versions of dimension reductions (with Adi Shraibman), Discrete Comput. Geom. 41 (2009), no. 2, 273--283.
• Lower bounds on quantum multiparty communication complexity (with T. Lee and A. Shraibman), proceedings of the 24th Conference on Computational Complexity, p. 254--262, 2009.
• Diamond graphs and super-reflexivity (with W.B. Johnson), J. Topol. Anal. 1 (2009), no. 2, 177--189.
• Tight embedding of subspaces of $L_p$ in $\ell_p^n$ for even $p$, Proc. AMS, 139 (2011), no. 12, 4419–4421.
• Commutators on $\L_p$, $1\leq p <\infty$ (with D. Dosev and W.B. Johnson), J. Amer. Math. Soc. 26 (2013), no. 1, 101–127.
• Approximate Gaussian isoperimetry for $k$ sets, GAFA Seminar 2006-2010, 373--379, Lecture Notes in Math., Vol 2050, Springer-Verlag (2012).
• Stabilizing isomorphisms from $\ell_p(\ell_2)$ into $L_p[0,1]$ (with R. Levy), Banach J. Math. Anal. 5 (2011), no. 2, 73–83.
• Dimension Reduction in $L_p$, $0<p<2$, was not sent for publication.
• Euclidean sections of convex bodies, series of lectures given in Bedlewo, Poland, July 6-12, 2008 and in Kent, Ohio, August 13-20, 2008, to appear.
• Bourgain's discretization Theorem, (with O. Gilady and A. Naor), to appear
• Deterministic Algorithms for Matrix Completion (with E. Heiman and A. Shraibman), to appear.
• Narrow and $\ell_2$-strictly singular operators from $L_p$ (with V. Mykhaylyuk, M. Popov and B. Randrianantoanina), submitted.
• Subspaces of $L_p$ that embed into $L_p(\mu)$ with $\mu$ finite (with W.B. Johnson), submitted.
• Matrix subspaces of $L_1$, submitted.

Last updated January, 2013