Funded Research Projects
Books
Publications
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Threshold for the measure of random polytopes
A survey (preprint).
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Inequalities 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.
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Threshold for the expected measure of random polytopes
with Silouanos Brazitikos and Minas Pafis, Mathematische Annalen 388 (2024), no. 3, 2991-3024.
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Half-space depth of log-concave probability measures
with Silouanos Brazitikos and Minas Pafis, Probability Theory and Related Fields 188 (2024), 309-336.
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Inequalities for the Radon transform on convex sets
with Alexander Koldobsky and Artem Zvavitch, International Mathematics Research Notices (2022), No. 18, 13984-14007.
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Continuous version of the approximate geometric Brascamp-Lieb inequalities
with Silouanos Brazitikos, Journal of Geometric Analysis 32 (2022), no. 6, 174.
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Norms 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.
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Volume difference inequalities
with Alexander Koldobsky, Transactions of the American Mathematical Society 370 (2018), 4351-4372.
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On the average volume of sections of convex bodies
with Silouanos Brazitikos, Susanna Dann and Alexander Koldobsky, Israel Journal of Mathematics 222 (2017), 921-947.
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Uniform 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.
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Inequalities for the surface area of projections of convex bodies
with Alexander Koldobsky and Petros Valettas, Canadian Journal of Mathematics 70 (2018), 804-823.
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Variants of the Busemann-Petty problem and of the Shephard problem
with Alexander Koldobsky, International Mathematics Research Notices (2017) No. 3, 921-943.
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Geometry of random sections of isotropic convex bodies
with Labrini Hioni and Antonis Tsolomitis, Bulletin of the Hellenic Mathematical Society 60 (2016), 20-40.
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Estimates for measures of lower dimensional sections of convex bodies
with Giorgos Chasapis and Dimitris-Marios Liakopoulos, Advances in Mathematics 306 (2017), 880-904.
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Euclidean regularization in John's position
with Giorgos Chasapis, Indiana University Mathematics Journal 65 (2016), 1877-1890.
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Remarks on an inequality of Rogers and Shephard
with Eleftherios Markessinis and Antonis Tsolomitis, Proceedings of the American Mathematical Society 144 (2016), 763-773.
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Asymptotic 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.
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M-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.
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Geometry 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.
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The isotropic position and the reverse Santalo inequality
with Grigoris Paouris and Beatrice-Helen Vritsiou, Israel Journal of Mathematics 203 (2014), 1-22.
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Quermassintegrals and asymptotic shape of random polytopes in an isotropic convex body
with Nikos Dafnis and Antonis Tsolomitis, Michigan Mathematical Journal 62 (2013), 59–79.
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A remark on the slicing problem
with Grigoris Paouris and Beatrice-Helen Vritsiou, Journal of Functional Analysis 262 (2012), 1062–1086.
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On 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.
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Psi(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.
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On the existence of subgaussian directions for log-concave measures
with Grigoris Paouris and Petros Valettas, Contemporary Mathematics 545 (2011), 103-122.
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On the isotropic constant of random polytopes
with Nikos Dafnis and Olivier Guedon, Advances in Geometry 10 (2010), 311-321.
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Asymptotic shape of a random polytope in a convex body
with Nikos Dafnis and Antonis Tsolomitis, Journal of Functional Analysis 257 (2009), 2820-2839.
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Threshold for the volume spanned by random points
with independent coordinates
with Dimitris Gatzouras, Israel Journal of Mathematics 169 (2009), 125-153.
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A note on subgaussian estimates for linear functionals
on convex bodies
with Alain Pajor and Grigoris Paouris, Proc. Amer. Math. Soc. 135 (2007), 2599-2606.
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On 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.
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A large deviations approach to the geometry
of random polytopes
with Dimitris Gatzouras, Mathematika 53 (2006), 173-211.
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Random points in isotropic unconditional convex bodies
with Marianna Hartzoulaki and Antonis Tsolomitis,
Journal of the London Mathematical Society 72
(2005), 779-798.
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Asymptotic formulas for the diameter of sections of
symmetric convex bodies
with Vitali Milman and Antonis Tsolomitis,
Journal of Functional Analysis 223
(2005), 86-108.
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Lower 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.
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Asymptotic 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.
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Some inequalities about mixed volumes
with Matthieu Fradelizi and Mathieu Meyer,
Israel Journal of Mathematics 135
(2003), 157-179.
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Volume radius of a random polytope in a convex body
with Antonis Tsolomitis,
Math. Proc. Cambridge Philos. Soc. 134
(2003), 13-21.
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On the volume ratio of two convex bodies
with Marianna Hartzoulaki, Bull. London
Math. Soc. 34 (2002), 703-707.
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Random spaces generated by vertices
of the cube
with Marianna Hartzoulaki, Discrete Comput. Geom.
28 (2002), 255-273.
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On a local version of the Aleksandrov-Fenchel inequalities
for the quermassintegrals of a convex body,
with Marianna Hartzoulaki and Grigoris Paouris,
Proc. Amer. Math. Soc. 130 (2002), 2403-2412.
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Euclidean structure in finite dimensional spaces
with Vitali Milman, Handbook of the Geometry of Banach Spaces
(Johnson-Lindenstrauss eds.), Vol. 1 (2001), 707-779.
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John's theorem for an arbitrary pair of convex bodies
with Eirini Perissinaki and Antonis Tsolomitis,
Geometriae Dedicata 84 (2001), 63-79.
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Concentration property on probability spaces
with Vitali Milman, Advances in Mathematics 156 (2000),
77-106.
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Convex 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.
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Extremal problems and isotropic positions of convex bodies
with Vitali Milman, Israel J. Math., 117 (2000), 29-60.
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Isotropic surface area measures
with Michael Papadimitrakis, Mathematika 46 (1999), 1-13.
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p-Cross-section bodies
with Richard Gardner, Indiana Univ. Math. J. 48 (1999),
593-614.
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Mean width and diameter of proportional sections
of a symmetric convex body
with Vitali Milman, J. Reine Angew. Math. 497 (1998), 113-139.
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How 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.
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On the diameter of proportional sections of a symmetric
convex body
with Vitali Milman,
International Mathematics Research Notices (1997) 1, 5-19.
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Low M*-estimates on coordinate subspaces
with Vitali Milman,
Journal of Functional Analysis 147 (1997), 457-484.
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On some vector balancing problems
Studia Mathematica 122 (1997), 225-234.
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A proportional Dvoretzky-Rogers factorisation result
Proceedings of the AMS 124 (1996), 233-241.
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A 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.
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On the mean value of the area of a random polygon
in a plane convex body
Mathematika 39 (1992), 279-290.
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A 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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