**Sections of convex bodies through their centroid**,*Archiv der Mathematik*69 (1997), 515-522.**Hyperplane sections of convex bodies in isotropic position**,*Beiträge zur Algebra und Geometrie*40 (1999), No. 1, 163-183.**A short solution to the Busemann-Petty problem**,*Positivity*3 (1999), 95-100 (with Franck Barthe and Bernard Maurey)**Sectional bodies associated to a convex body**,*Proceedings of the American Mathematical Society*128 (2000), No. 9, 2735-2744.**Shift inequalities of Gaussian type and norms of barycenters**,*Studia Mathematica*146 (2001), 245-259 (with Franck Barthe and Dario Cordero-Erausquin).**Some inequalities about mixed volumes**,*Israel Journal of Mathematics*135 (2003), 157-179 (with Apostolos Giannopoulos and Mathieu Meyer).**The**,*(B)*-conjecture for the Gaussian measure of dilates of symmetric convex sets and related problems*Journal of Functional Analysis*214 (2004), 410-427 (with Dario Cordero-Erausquin and Bernard Maurey).**Two-point symmetrization and convexity,***Archiv der Mathematik*82 (2004), 282-288 (with Guillaume Aubrun).**The extreme points of subsets of**,*s*-concave probabilies and a geometric localization theorem*Discrete and Computational Geometry*31 (2004), 327-335 (with Olivier Guédon).**A generalized localization theorem and geometric inequalities for convex bodies**,*Advances in Mathematics*204 (2006), 509-529 (with Olivier Guédon).**Some functional forms of Blaschke-Santaló inequality**,*Mathematische Zeitschrift*256 (2007), 379-395 (with Mathieu Meyer).**Some functional inverse Santaló inequalities**,*Advances in Mathematics*218 (2008), 1430-1452 (with Mathieu Meyer).**Increasing functions and inverse Santaló inequality for unconditional functions**,*Positivity*12 (2008), 407-420 (with Mathieu Meyer).**Concentration inequalities for**,*s*-concave measures of dilations of Borel sets and applications*Electronic Journal of Probability*Vol. 14 (2009), Paper no. 71, 2068-2090.**The case of equality for an inverse Santaló functional inequality**,*Advances in Geometry*10 (2010), 621--630 (with Yehoram Gordon, Mathieu Meyer and Shlomo Reisner).**Functional inequalities related to Mahler conjecture**,*Monatshefte für Mathematik*159, No. 1-2 (2010), 13-25 (with Mathieu Meyer).**An application of shadow systems to Mahler's conjecture**,*Discrete and Computational Geometry*48 (2012), no. 3, 721-734 (with Mathieu Meyer and Artem Zvavitch).**Simplices in the Euclidean ball**,*Canadian Mathematical Bulletin*55 (2012), 498-508 (with Grigoris Paouris and Carsten Schütt).**The volume product of convex bodies with many hyperplane symmetries**,*American Journal of Mathematics*135 (2013), 1-37 (with Franck Barthe).**Stability of the functional forms of the Blaschke-Santaló inequality**,*Monatshefte für Mathematik*173 (2014), 135-159, (with Franck Barthe and Karoly Böröczky Jr.).**On the analogue of the concavity of entropy power in the Brunn-Minkowski theory**,*Advances in Applied Mathematics*57 (2014), 1-20, (with Arnaud Marsiglietti).**Thin-shell concentration for convex measures**,*Studia Mathematica*223 (2) (2014), 123-148, (with Olivier Guédon and Alain Pajor).**Volume of the polar of random sets and shadow systems**,*Mathematische Annalen*362 (2015), 1305-1325, (with Dario Cordero-Erausquin, Grigoris Paouris and Peter Pivovarov).**Functional versions of $L_p$-affine surface area and entropy inequalities**,*International Mathematics Research Notices*(2016) Vol. 2016, 1223-1250, doi: 10.1093/imrn/rnv151, (with Umut Caglar, Olivier Guédon, Joseph Lehec, Carsten Schütt and Elisabeth Werner).**Do Minkowski averages get progressively more convex?**,*C. R. Acad. Sci. Paris,*Ser. I 354 (2016) 185-189, (with Mokshay Madiman, Arnaud Marsiglietti and Artem Zvavitch).**Optimal Concentration of Information Content For Log-Concave Densities**, High Dimensional Probability VII, The Cargèse Volume, Progress in Probability 71, Birkhauser (2016), 45-60, (with Mokshay Madiman and Liyao Wang).**On the volume of sections of a convex body by cones**,*Proceedings of the American Mathematical Society*145 (7) (2017), 3153-3164 (with Mathieu Meyer and Vlad Yaskin).**The convexification effect of Minkowski summation**,*EMS Surveys in Mathematical Sciences*5 (2018), 1-64, (with Mokshay Madiman, Arnaud Marsiglietti and Artem Zvavitch).**Polytopes of Maximal Volume Product**,*Discrete and Computational Geometry*62 (3) (2019), 583-600, DOI 10.1007/s00454-019-00072-3, (with Matthew Alexander and Artem Zvavitch).**Concentration of information content for convex measures**, expanded version (from 5 to 22 pages) of the conference version.*Electronic Journal of Probability*, 25 (2020) paper no. 20, 22 pp. (with Jiange Li and Mokshay Madiman).**Random polytopes and the wet part for arbitrary probability distributions**.*Annales Henri Lebesgue*, Vol. 3 (2020), pp. 701-715, (with Imre Bárány, Xavier Goaoc, Alfredo Hubard and Günter Rote)**Geometry and volume product of finite dimensional Lipschitz-free spaces**,*Journal of Functional Analysis*280 (2021) 108849 (with Matthew Alexander, Luis Carlos Garcia-Lirola and Artem Zvavitch).**Equipartitions and Mahler volume of symmetric convex bodies**, (with Alfredo Hubard, Mathieu Meyer, Edgardo Roldán-Pensado and Artem Zvavitch). To appear in*American Journal of Mathematics*. Preprint July 2019.**Volume of the Minkowski sums of star-shaped sets**, (with Zsolt Lángi and Artem Zvavitch). Submitted. Preprint October 2019.**The functional form of Mahler conjecture for even log-concave functions in dimension 2**, (with Elie Nakhle). Submitted. Preprint January 2021.

**Concentration of information content for convex measures**, Proceedings of the 2016 IEEE International Symposium on Information Theory (ISIT), 1128-1132. DOI: 10.1109/ISIT.2016.7541475. (with Jiange Li and Mokshay Madiman).**Usable deviation bounds for the information content of convex measures**, 2020 IEEE International Symposium on Information Theory (ISIT), Los Angeles, CA, USA, 2020, pp. 2258-2263. (with Jiange Li and Mokshay Madiman).