Galyna V. Livshyts
Welcome to my webpage! I am an Assistant professor at the Mathematics Department at Georgia Institute of Technology. I work in Asymptotic Analysis and
Convex geometry, which means that I like a lot the following areas of math: Geometric Analysis, Random matrix theory, Probability, Harmonic Analysis, Discrete and Combinatorial geometry. This research is supported by NSF CAREER DMS-1753260.
E-mail:
glivshyts6@math.gatech.edu
Address: Room 228, Skiles bldg, located at 686 Cherry street NW, Atlanta, GA, 30332.
G. V. Livshyts, On a conjectural symmetric version of Ehrhard's inequality, preprint.
A. V. Kolesnikov, G. V. Livshyts, On the Local version of the Log-Brunn-Minkowski conjecture and some new related geometric inequalities, submitted. See also slides and video.
J. Hosle, A. V. Kolesnikov, G. V. Livshyts, On the L_p-Brunn-Minkowski and dimensional Brunn-Minkowski conjectures for log-concave measures, Journal of Geometric Analysis (2020), https://doi.org/10.1007/s12220-020-00505-z.. See also slides and video.
J. Hao, H. Huang, G. V. Livshyts, K. Tikhomirov, Distribution of the minimal distance of random linear codes, submitted.
G. V. Livshyts, K. Tikhomirov, R. Vershynin, The smallest singular value of inhomogeneous square random matrices, to appear in Annals of Probability. 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, accepted to Journal d'Analyse Mathematique. 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.
A. V. Kolesnikov, G. V. Livshyts, On the Gardner-Zvavitch conjecture: symmetry in the inequalities of Brunn-Minkowski type, accepted to Advances in Math. 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.
Differential Geometry (Spring 2020, graduate)
Introduction to Probability and Statistics (Fall 2019, undergraduate)
Applied Combinatorics (Fall 2019, distance learning)
Analysis II (Spring 2019, undergraduate)
Putnam preparation (Fall 2018, undergraduate)
Analysis I (Fall 2018, undergraduate)
REU with Johannes Hosle (UCLA), Summer 2018, resulting in this paper
Linear algebra (Spring 2018, undergraduate)
High-dimensional geometry and probability (Spring 2018, graduate topics course)
Probability II (Spring 2017, graduate)
Probability I (Fall 2016, graduate)
PUTNAM preparation (Fall 2016, undergraduate)
The William Lowell Putnam Mathematical Competition is an annual mathematics competition for undergraduate college students enrolled at institutions of higher learning in the United States and Canada. It awards a scholarship and cash prizes ranging from $250 to $2,500 for the top students and $5,000 to $25,000 for the top schools. It is widely considered to be the most prestigious university-level mathematics examination in the world.
The competition was founded in 1927 by Elizabeth Lowell Putnam in memory of her husband William Lowell Putnam. The exam has been offered annually since 1938 and is administered by the Mathematical Association of America.
See the oficial webpage of the PUTNAM competition, as well as the page containing PUTNAM problems and solutions of the recent years.
All of the Georgia Tech students interested in participating PUTNAM, and/or joining my class aimed to prepare for the competition, which runs on Tuesdays 3:05-4:55 pm at 171 skiles, are more then welcome to get in touch with me via e-mail, or stop by my office 228 Skiles, or to just show up in class!
Below please see some materials for the course.
Introduction to Probability and Statistics (Fall 2015, undergraduate)
My husband Benjamin Jaye is also a mathematician. He also works at Georgia Tech.