Funded Research Projects
Research Training Network "Phenomena in High Dimensions" (MRTN-CT-2004-511953)
Asymptotic Theory of Convex Bodies "ARISTEIA II- ATOCB - 3566" (General Secretariat of Research and Technology, Greece)
Geometric Functional Analysis and Applications "ELIDEK- GFAA - 1849" (Hellenic Foundation for Research and Innovation)
Books
Geometry of isotropic convex bodies
with Silouanos Brazitikos, Petros Valettas and Beatrice-Helen Vritsiou
AMS-Mathematical Surveys and Monographs 196 (2014).Asymptotic Geometric Analysis, Part I
with Shiri Artstein-Avidan and Vitali Milman
AMS-Mathematical Surveys and Monographs 202 (2015).Asymptotic Geometric Analysis, Part II
with Shiri Artstein-Avidan and Vitali Milman
AMS-Mathematical Surveys and Monographs 261 (2021).
Publications
On the maximal perimeter of isotropic log-concave probability measures
with Silouanos Brazitikos, Antonios Hmadi and Natalia Tziotziou, Preprint.
Regular functional covering numbers
with Natalia Tziotziou, Preprint.
The isotropic constant in the theory of high-dimensional convex bodies
with Minas Pafis and Natalia Tziotziou, Bulletin of the Hellenic Mathematical Society 69 (2025), 89-188.
Moments of the Cramer transform of log-concave probability measures
with Natalia Tziotziou, Preprint.
Threshold for the measure of random polytopes
Courses in Discrete and Computational Geometry, Bolyai Society Mathematical Studies, Vol. 31, to appear.
pdfInequalities for sections and projections of convex bodies
with Alexander Koldobsky and Artem Zvavitch, Harmonic Analysis and Convexity (edited by A. Koldobsky and A. Volberg), Advances in Analysis and Geometry, Vol. 9, De Gruyter, 2023.
pdfThreshold for the expected measure of random polytopes
with Silouanos Brazitikos and Minas Pafis, Mathematische Annalen 388 (2024), no. 3, 2991-3024.
pdfHalf-space depth of log-concave probability measures
with Silouanos Brazitikos and Minas Pafis, Probability Theory and Related Fields 188 (2024), 309-336.
pdfInequalities for the Radon transform on convex sets
with Alexander Koldobsky and Artem Zvavitch, International Mathematics Research Notices (2022), No. 18, 13984-14007.
pdfContinuous version of the approximate geometric Brascamp-Lieb inequalities
with Silouanos Brazitikos, Journal of Geometric Analysis 32 (2022), no. 6, 174.
pdfNorms of weighted sums of log-concave random vectors
with Giorgos Chasapis and Nikos Skarmogiannis, Communications in Contemporary Mathematics 22 (2020), no. 4, 1950036, 31 pp.
pdfVolume difference inequalities
with Alexander Koldobsky, Transactions of the American Mathematical Society 370 (2018), 4351-4372.
pdfOn the average volume of sections of convex bodies
with Silouanos Brazitikos, Susanna Dann and Alexander Koldobsky, Israel Journal of Mathematics 222 (2017), 921-947.
pdfUniform cover inequalities for the volume of coordinate sections and projections of convex bodies
with Silouanos Brazitikos and Dimitris-Marios Liakopoulos, Advances in Geometry 18 (2018), 345-354.
pdfInequalities for the surface area of projections of convex bodies
with Alexander Koldobsky and Petros Valettas, Canadian Journal of Mathematics 70 (2018), 804-823.
pdfVariants of the Busemann-Petty problem and of the Shephard problem
with Alexander Koldobsky, International Mathematics Research Notices (2017) No. 3, 921-943.
pdfGeometry of random sections of isotropic convex bodies
with Labrini Hioni and Antonis Tsolomitis, Bulletin of the Hellenic Mathematical Society 60 (2016), 20-40.
pdfEstimates for measures of lower dimensional sections of convex bodies
with Giorgos Chasapis and Dimitris-Marios Liakopoulos, Advances in Mathematics 306 (2017), 880-904.
pdfEuclidean regularization in John's position
with Giorgos Chasapis, Indiana University Mathematics Journal 65 (2016), 1877-1890.
pdfRemarks on an inequality of Rogers and Shephard
with Eleftherios Markessinis and Antonis Tsolomitis, Proceedings of the American Mathematical Society 144 (2016), 763-773.
pdfAsymptotic shape of the convex hull of isotropic log-concave random vectors
with Labrini Hioni and Antonis Tsolomitis, Advances in Applied Mathematics 75 (2016), 116-143.
pdfM-estimates for isotropic convex bodies and their L_q centroid bodies
with Emanuel Milman, in Geometric Aspects of Functional Analysis, Lecture Notes in Mathematics 2116 (2014), 159-182.
pdfGeometry of the L_q centroid bodies of an isotropic log-concave measure
with Pantelis Stavrakakis, Antonis Tsolomitis and Beatrice-Helen Vritsiou, Transactions of the American Mathematical Society 367 (2015), 4569-4593.
pdfThe isotropic position and the reverse Santalo inequality
with Grigoris Paouris and Beatrice-Helen Vritsiou, Israel Journal of Mathematics 203 (2014), 1-22.
pdfQuermassintegrals and asymptotic shape of random polytopes in an isotropic convex body
with Nikos Dafnis and Antonis Tsolomitis, Michigan Mathematical Journal 62 (2013), 59–79.
pdfA remark on the slicing problem
with Grigoris Paouris and Beatrice-Helen Vritsiou, Journal of Functional Analysis 262 (2012), 1062–1086.
pdfOn the distribution of the psi(2)-norm of linear functionals on isotropic convex bodies
with Grigoris Paouris and Petros Valettas, in Geometric Aspects of Functional Analysis, Lecture Notes in Mathematics 2050 (2012), 227-253.
pdfPsi(a)-estimates for marginals of log-concave probability measures
with Grigoris Paouris and Petros Valettas, Proceedings of the American Mathematical Society 140 (2012), 1297-1308.
pdfOn the existence of subgaussian directions for log-concave measures
with Grigoris Paouris and Petros Valettas, Contemporary Mathematics 545 (2011), 103-122.
pdfOn the isotropic constant of random polytopes
with Nikos Dafnis and Olivier Guedon, Advances in Geometry 10 (2010), 311-321.
pdfAsymptotic shape of a random polytope in a convex body
with Nikos Dafnis and Antonis Tsolomitis, Journal of Functional Analysis 257 (2009), 2820-2839.
pdfThreshold for the volume spanned by random points with independent coordinates
with Dimitris Gatzouras, Israel Journal of Mathematics 169 (2009), 125-153.
pdfA note on subgaussian estimates for linear functionals on convex bodies
with Alain Pajor and Grigoris Paouris, Proceedings of the American Mathematical Society 135 (2007), 2599-2606.
pdfOn the maximal number of facets of 0/1 polytopes
with Dimitris Gatzouras and Nikos Markoulakis, in Geometric Aspects of Functional Analysis, Lecture Notes in Mathematics 1910 (2007), 117-125.
pdfA large deviations approach to the geometry of random polytopes
with Dimitris Gatzouras, Mathematika 53 (2006), 173-211.
pdfRandom points in isotropic unconditional convex bodies
with Marianna Hartzoulaki and Antonis Tsolomitis, Journal of the London Mathematical Society 72 (2005), 779-798.
pdfAsymptotic formulas for the diameter of sections of symmetric convex bodies
with Vitali Milman and Antonis Tsolomitis, Journal of Functional Analysis 223 (2005), 86-108.
pdfLower bound for the maximal number of facets of a 0/1 polytope
with Dimitris Gatzouras and Nikos Markoulakis, Discrete and Computational Geometry 34 (2005), 331-349.
pdfAsymptotic convex geometry: a short overview
with Vitali Milman, Different Faces of Geometry (Donaldson-Eliashberg-Gromov eds.), Int. Math. Series Vol. 3, Kluwer, New York (2004), 87-162.
pdfSome inequalities about mixed volumes
with Matthieu Fradelizi and Mathieu Meyer, Israel Journal of Mathematics 135 (2003), 157-179.
pdfVolume radius of a random polytope in a convex body
with Antonis Tsolomitis, Mathematical Proceedings of the Cambridge Philosophical Society 134 (2003), 13-21.
pdfOn the volume ratio of two convex bodies
with Marianna Hartzoulaki, Bulletin of the London Mathematical Society 34 (2002), 703-707.
pdfRandom spaces generated by vertices of the cube
with Marianna Hartzoulaki, Discrete and Computational Geometry 28 (2002), 255-273.
pdfOn a local version of the Aleksandrov-Fenchel inequalities for the quermassintegrals of a convex body,
with Marianna Hartzoulaki and Grigoris Paouris, Proceedings of the American Mathematical Society 130 (2002), 2403-2412.
pdfEuclidean structure in finite dimensional spaces
with Vitali Milman, Handbook of the Geometry of Banach Spaces (Johnson-Lindenstrauss eds.), Vol. 1 (2001), 707-779.
pdfJohn's theorem for an arbitrary pair of convex bodies
with Eirini Perissinaki and Antonis Tsolomitis, Geometriae Dedicata 84 (2001), 63-79.
pdfConcentration property on probability spaces
with Vitali Milman, Advances in Mathematics 156 (2000), 77-106.
pdfConvex bodies with minimal mean width
with Vitali Milman and M. Rudelson, in Geometric Aspects of Functional Analysis, Lecture Notes in Mathematics 1745 (2000), 81-93.
pdfExtremal problems and isotropic positions of convex bodies
with Vitali Milman, Israel Journal of Mathematics 117 (2000), 29-60.
pdfIsotropic surface area measures
with Michael Papadimitrakis, Mathematika 46 (1999), 1-13.
pdfp-Cross-section bodies
with Richard Gardner, Indiana Univ. Math. J. 48 (1999), 593-614.
pdfMean width and diameter of proportional sections of a symmetric convex body
with Vitali Milman, J. Reine Angew. Math. 497 (1998), 113-139.
pdfHow small can the intersection of a few rotations of a symmetric convex body be?
with Vitali Milman, C.R. Acad. Sci. Paris 325 (1997), 389-394.
pdfOn the diameter of proportional sections of a symmetric convex body
with Vitali Milman, International Mathematics Research Notices (1997) 1, 5-19.
pdfLow M*-estimates on coordinate subspaces
with Vitali Milman, Journal of Functional Analysis 147 (1997), 457-484.
pdfOn some vector balancing problems
Studia Mathematica 122 (1997), 225-234.
pdfA proportional Dvoretzky-Rogers factorisation result
Proceedings of the American Mathematical Society 124 (1996), 233-241.
pdfA note on the Banach-Mazur distance to the cube
Geometric aspects of functional analysis (Lindenstrauss-Milman eds.), Operator Theory: Advances and Applications, Vol. 77 (1995), 67-73.
pdfOn the mean value of the area of a random polygon in a plane convex body
Mathematika 39 (1992), 279-290.
pdfA note on a problem of H. Busemann and C.M. Petty concerning sections of symmetric convex bodies
Mathematika 37 (1990), 239-244.
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