Alexey Glazyrin Professor Address University of Texas Rio Grande Valley School of Mathematical & Statistical Sciences One West University Blvd, BLHSB 2.520 Brownsville, TX 78520 E-mail Alexey.Glazyrin@utrgv.edu Phone +19568826610

General Information

I got my Ph.D. in Mathematics in 2009 from Moscow State University. My dissertation advisor was Nikolay Dolbilin.

My research interests include discrete and computational geometry, geometry of numbers, combinatorics. My Google Scholar profile is here

More information is available in my CV.

Teaching

In Fall 2023 I teach the undergraduate course of Differential Equations and the graduate course of Topology. All course materials are available at the Blackboard. My scheduled office hours are 3:00-4:30 pm on Monday and Wednesday.

Conference

I am one of the organizers of the Discrete Geometry and Algebraic Combinatorics Conference on South Padre Island, TX. Check the website of the conference for more details.

Papers

Preprints

• On the total perimeter of disjoint convex bodies (with Arseniy Akopyan), arXiv:2308.16340

• Note on illuminating constant width bodies, arXiv:2305.04485

• Optimal measures for multivariate geometric potentials (with Dmitriy Bilyk, Damir Ferizović, Ryan Matzke, Josiah Park, Oleksandr Vlasiuk), arXiv:2303.14258

• Optimizers of three-point energies and nearly orthogonal sets (with Dmitriy Bilyk, Damir Ferizović, Ryan Matzke, Josiah Park, Oleksandr Vlasiuk), arXiv:2303.12283

• Extensions of polynomial plank covering theorems (with Roman Karasev and Alexandr Polyanskii), arXiv:2211.10886

• On the size of maximal binary codes with 2, 3, and 4 distances (with Alexander Barg, Wei-Jiun Kao, Ching-Yi Lai, Pin-Chieh Tseng, Wei-Hsuan Yu), arXiv:2210.07496

• Moments of isotropic measures and optimal projective codes, arXiv:1904.11159

• Stability of optimal spherical codes (with Károly J. Böröczky), arXiv:1711.06012

Journal publications

• Covering by planks and avoiding zeros of polynomials (with Roman Karasev and Alexandr Polyanskii), International Mathematics Research Notices, 13(2023), pp. 11684-11700, arXiv:2112.05382

• Potential theory with multivariate kernels (with Dmitriy Bilyk, Damir Ferizović, Ryan Matzke, Josiah Park, Oleksandr Vlasiuk), Mathematische Zeitschrift, 301 (3) (2022), pp. 2907-2935, arXiv:2104.03410

• Optimal measures for p-frame energies on spheres (with Dmitriy Bilyk, Ryan Matzke, Josiah Park, Oleksandr Vlasiuk), Revista Matemática Iberoamericana, 38 (4) (2022), pp. 1129-1160, arXiv:1908.00885

• A short solution of the kissing number problem in dimension three, Discrete & Computational Geometry, 69(3) (2023), pp. 931-935, arXiv:2012.15058, supplementary file with inequalities

• Domes over curves (with Igor Pak), International Mathematics Research Notices, 18 (2022), pp. 14067-14104, arXiv:2005.02555

• Covering by homothets and illuminating convex bodies, Proceedings of the American Mathematical Society, 150 (02) (2022), pp. 779-793, arXiv:1905.10516

• Hexagon tilings of the plane that are not edge-to-edge (with Dirk Frettlöh and Zsolt Lángi), Acta Mathematica Hungarica, 164 (2021), pp. 341- 349, arXiv:1911.12752

• Energy on spheres and discreteness of minimizing measures (with Dmitriy Bilyk, Ryan Matzke, Josiah Park, Oleksandr Vlasiuk), Journal of Functional Analysis, 280(11) (2021), 108995, arXiv:1908.10354

• Repeated minimizers of p-frame energies (with Josiah Park), SIAM Journal on Discrete Mathematics, 34(4) (2020), pp. 2411-2423, arXiv:1901.06096

• Contact graphs of ball packings, Journal of Combinatorial Theory, Series B, 145 (2020), pp. 323-340, arXiv:1707.02526

• Covering a ball by smaller balls, Discrete & Computational Geometry, 62(4) (2019), pp. 781-787, doi:10.1007/s00454-018-0010-4, covering balls.pdf (first version)

• Upper bounds on s-distance sets and equiangular lines (with Wei-Hsuan Yu), Advances in Mathematics, Volume 330 (2018), pp. 810-833, arXiv:1611.09479

• Stability of the simplex bound for packings by equal spherical caps determined by simplicial regular polytopes (with Károly Böröczky, Károly J. Böröczky, Ágnes Kovács) In: Conder M., Deza A., Weiss A. (eds) Discrete Geometry and Symmetry. GSC 2015. Springer Proceedings in Mathematics & Statistics, vol 234. Springer (Volume dedicated to the 60th anniversary of Professors Károly Bezdek and Egon Schulte), 2018, pp. 31-60, arXiv:1711.00211
• The Voronoi functional is maximized by the Delaunay triangulation in the plane (with Herbert Edelsbrunner, Oleg Musin, Anton Nikitenko), Combinatorica, Volume 37, Issue 5 (2017), pp. 887-910, arXiv:1411.6337
• Finite two-distance tight frames (with Alexander Barg, Wei-Hsuan Yu, Kasso Okoudjou), Linear Algebra and its Applicatoins, Volume 475 (2015), pp. 163-175, arXiv:1402.3521
• On maximum volume simplices in polytopes (with Arseniy Akopyan), Periodica Mathematica Hungarica, Volume 69, Issue 2 (2014), pp. 251-256, doi:10.1007/s10998-014-0051-2
• Functionals on triangulations of Delaunay sets (with Nikolay Dolbilin, Herbert Edelsbrunner, Oleg Musin), Moscow Mathematical Journal, Volume 14, Number 3 (2014), pp. 491-504, arXiv:1211.7053
• Upper bounds for the perimeter of plane convex bodies (with Filip Morić), Acta Mathematica Hungarica, Volume 142, Issue 2 (2014), pp. 366-383, doi:10.1007/s10474-013-0350-8
• Lower bounds for the simplexity of the n-cube, Discrete Mathematics, Volume 312, Issue 24 (2012), pp. 3656-3662, arXiv:0910.4200
• The extremal spheres theorem (with Arseniy Akopyan, Oleg Musin, Alexey Tarasov), Discrete Mathematics, Volume 311, Issues 2-3 (2011), pp. 171-177, arXiv:0906.3823
• On simplicial partitions of polytopes, Mathematical Notes, 85:6 (2009), pp. 799-806, doi:10.1134/S0001434609050228
• Anti-Dürer conjecture for non-convex polytopes (with Alexey Tarasov), Russian Mathematical Surveys, 64:3 (2009), pp. 573-574, doi:10.1070/RM2009v064n03ABEH004623
• The lonely vertex problem (with Dirk Frettlöh), Beiträge zur Algebra und Geometrie, Vol. 50 (2009), No. 1, pp. 71-79, arXiv:0710.4870

Proceedings and extended abstracts

• Price of SDP relaxations for spherical codes (Designs, Codes, Graphs and Related Areas) (with O.Musin), RIMS Kokyuroku, Volume 1889, 2014, pp. 1-6
• Functionals on triangulations of Delaunay sets (with N.Dolbilin, H.Edelsbrunner, O.Musin), Yaroslavl International Conference Geometry, Topology, and Applications, September 23-27, 2013. Abstracts, Yaroslavl, 2013, 33-37
• Optimality of functionals on Delaunay triangulations (with N.Dolbilin, H.Edelsbrunner, O.Musin), Proceedings of the workshop on distance geometry and applications, Manaus, Brazil, 115-118, June 24-27, 2013
• On new property of polyhedral tilings, Proc. Ninth International Seminar Discrete Mathematics and its Applications, 377-379, 2007
• Triangulations of 2-layers polytopes, Proceedings of Second COE Workshop on Sphere Packings, 90-94, May 30 - June 3, 2005
• Rigidity of some classes of cubillages (with A. Garber), Proceedings of Second COE Workshop on Sphere Packings, 86-89, May 30 - June 3, 2005