A. Colesanti, A. V. Kolesnikov, G. V. Livshyts, L. Rotem, On Weighted Blaschke-Santalo and strong Brascamp-Lieb inequalities, preprint.
A. Colesanti, E. Francini, G. V. Livshyts, P. Salani, The Brunn-Minkowski inequality for the first eigenvalue of the Ornstein-Uhlenbeck operator and log-concavity of the relevant eigenfunction, submitted.
O. Herscovici, G. V. Livshyts, L. Rotem, A. Volberg, Stability and the equality case in the B-theorem, submitted.
O. Herscovici, G. V. Livshyts, Kohler-Jobin meets Ehrhard: the sharp lower bound for the Gaussian principal frequency while the Gaussian torsional rigidity is fixed, via rearrangements, to appear in Proceedings of the AMS.
A.E. Litvak, G. V. Livshyts, New bounds on the minimal dispersion, J. of Complexity, 72 (2022), 101648.
G. Bonnet, D. Dadush, U. Grupel, S. Huberts, G. V. Livshyts, Combinatorial diameter of random polytopes, 38th Symposium on Computational Geometry (SoCG 2022).
G. V. Livshyts, A universal bound in the dimensional Brunn-Minkowski inequality for log-concave measures, Trans. Amer. Math. Soc. 376 (2023), 6663-6680.
G. V. Livshyts, On a conjectural symmetric version of Ehrhard's inequality, to appear in Trans. Amer. Math. Soc.
A. V. Kolesnikov, G. V. Livshyts, On the Local version of the Log-Brunn-Minkowski conjecture and some new related geometric inequalities,
International Mathematics Research Notices, 142, 08 June 2021. See also slides and
video
or this (better!) board and video.
Remark: Proposition 6.3 in the initial version was incorrect, see corrected version here:
updated version. This proposition is non essential and unrelated to any of the the main results.
J. Hosle, A. V. Kolesnikov, G. V. Livshyts, On the L_p-Brunn-Minkowski and dimensional Brunn-Minkowski conjectures for log-concave measures, The Journal of Geometric Analysis 31 (6), 5799-5836, (2020). See also slides and video.
J. Hao, H. Huang, G. V. Livshyts, K. Tikhomirov, Distribution of the minimal distance of random linear codes, IEEE Transactions on Information Theory 68 (10), 6388-6401, (2022).
G. V. Livshyts, K. Tikhomirov, R. Vershynin, The smallest singular value of inhomogeneous square random matrices, Ann. Probab. 49 (2021), no. 3, 1286-1309. See also slides.
G. V. Livshyts, Some remarks about the maximal perimeter of convex sets with respect to probability measures, Commun. Contemp. Math., (2020), https://doi.org/10.1142/S0219199720500376. See also slides.
B. Jaye, G. V. Livshyts, G. Paouris, P. Pivovarov, Remarks on the Renyi entropy of a sum of i.i.d. random variables, IEEE Trans. Inform. Theory 66 (2020), no. 5, 2898-2903. 94A17 (60E15).
G. V. Livshyts, The smallest singular value of heavy-tailed not necessarily i.i.d. random matrices via random rounding, Journal d'Analyse Mathematique, 145 (1), 257-306, (2021). See also slides (the same file as three rows above).
Bo'az Klartag, G. V. Livshyts, The lower bound for Koldobsky's slicing inequality via random rounding, Israel Seminar (GAFA) 2017-2019 Volume II, (2020), p. 43-63. See also some photos by Marton Naszodi.
[Erratum: in 2023, Julian Haddad spotted a technical error in the published version of the paper; this error has been fixed in the current arXiv version, posted July 18, 2023.]
A. V. Kolesnikov, G. V. Livshyts, On the Gardner-Zvavitch conjecture: symmetry in the inequalities of Brunn-Minkowski type, Ad- vances in Mathematics 384 (2021) 107689. See also slides and video.
A. Colesanti, G. V. Livshyts, A note on the quantitative local version of the Log-Brunn-Minkowski inequality, Advances in Analysis and Geometry 2, special volume dedicated to the mathematical legacy of Victor Lomonosov, ISBN: 978-3-11-065339-7, (2020).
G. V. Livshyts, K. Tikhomirov, Cube is a strict local maximizer for the illumination number, Discrete and Computational Geometry, (2019), 63(1), 209-228.
G. V. Livshyts, An extension of Minkowski's theorem and its applications to questions about projections for measures, Advances in Mathematics, Volume 356, 7 November 2019, 106803. See also slides.
G. V. Livshyts, K. Tikhomirov, Randomized coverings of a convex body with its homothetic copies, and illumination, Proceedings of the AMS, (2019), ISSN 1088-6826(online), ISSN 0002-9939(print).
A. Colesanti, G. V. Livshyts, A. Marsiglietti, On the stability of Brunn-Minkowski type inequalities, Journal of Functional Analysis 273 (2017), no. 3, 1120-1139. See also video.
G. Livshyts, A. Marsiglietti, P. Nayar, A. Zvavitch, On the Brunn-Minkowski inequality for general measures with applications to new isoperimetric type-inequalities, Transactions of the AMS, 369 (2017), no. 12, 8725-8742.
G. Livshyts, P. Paouris, P. Pivovarov, On sharp bounds for marginal densities of product measures, Israel Journal of Mathematics, (2016), 216(2), 877-889. See also slides.
G. V. Livshyts, Surface area of polytopes with respect to log-concave rotation invariant measures, Adv. Appl. Math., vol. 70, 54-69, (2015).
See also slides from my thesis defense.
G. V. Livshyts, Maximal Surface Area of a convex set in Rn with respect to log concave rotation invariant measures, GAFA Seminar Notes, 2116, (2014), 355-384. See also slides and video.
G. V. Livshyts, Maximal surface area of a convex set in Rn with respect to exponential rotation invariant measures, J. Math. Anal. Appl., 404, 2, (2013), 231-238.
