In Fall 2019 I teach the graduate course of Algebra I. All course materials are available at the Blackboard. My scheduled office hours are 12:00-1:00 pm on Monday and Wednesday and 5:00-6:00 pm on Tuesday and Thursday.
Conference
I am one of the organizers of the annual Discrete Geometry and Algebraic Combinatorics Conference on South Padre Island, TX. Check the website of the conference for more details.
Papers
Preprints
Energy on spheres and discreteness of minimizing measures (with Dmitriy Bilyk, Ryan Matzke, Josiah Park, Oleksandr Vlasiuk), arXiv:1908.10354
Optimal measures for p-frame energies on spheres (with Dmitriy Bilyk, Ryan Matzke, Josiah Park, Oleksandr Vlasiuk), arXiv:1908.00885
Covering by homothets and illuminating convex bodies, arXiv:1905.10516
Moments of isotropic measures and optimal projective codes, arXiv:1904.11159
Repeated minimizers of p-frame energies (with Josiah Park), arXiv:1901.06096
Stability of optimal spherical codes (with Károly J. Böröczky), arXiv:1711.06012
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) to appear in Volume dedicated to the 60th anniversary of Professors Károly Bezdek and Egon Schulte, Springer Contributed Volume on Discrete Geometry and Symmetry, Springer (2017), arXiv:1711.00211
The Voronoi functional is maximized by the Delaunay triangulation in the plane (with H. Edelsbrunner, O. Musin, A. Nikitenko), Combinatorica, Volume 37, Issue 5 (2017), pp. 887-910 arXiv:1411.6337
Finite two-distance tight frames (with A. Barg, W.-H. Yu, K. Okoudjou), Linear Algebra and its Applicatoins, Volume 475 (2015), pp. 163-175, arXiv:1402.3521
On maximum volume simplices in polytopes (with A. 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 N. Dolbilin, H. Edelsbrunner, O. 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 F. 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 A. Akopyan, O. Musin, A. Tarasov), Discrete Mathematics, Volume 311, Issues 2-3 (2011), pp. 171-177, arXiv:0906.3823
Anti-Dürer conjecture for non-convex polytopes (with A. Tarasov), Russian Mathematical Surveys, 64:3 (2009), pp. 573-574, doi:10.1070/RM2009v064n03ABEH004623
The lonely vertex problem (with D. 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