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Alexey Garber

Assistant Professor

Ph.D. (2009, Steklov Mathematical Institute, Russian Academy of Sciences)

Contact information:

LHSB 2.518
School of Mathematical & Statistical Sciences
1 West University blvd.
The University of Texas Rio Grande Valley
Brownsville, TX, 78520

tel: +1 956 882 6672

e-mail: alexey.garber@utrgv.edu

General information

Research

I am working on different problems of discrete geometry and combinatorics. My current research interests are parallelohedra theory (in particular, the Voronoi conjecture on parallelohedra), geometrical properties of quasiperiodic point sets (bounded distance and bilipschitz equivalence to a lattice), and measures equipartitions.

You can find some more structured information below, or in my CV.

Teaching

Currently (Spring 2020) I am teaching the following courses:

  • MATH 2318-11 Linear Algebra;
  • MATH 4390-06 Math Project.
Publications and preprints

Last updated in 2020.

Preprints

  1. A. Garber, I. Pak, Concrete polytopes may not tile the space, preprint, arXiv:2003.04667, 2020.
  2. N. Dolbilin, A. Garber, U. Leopold, E. Schulte, On the regularity radius of Delone sets in R3, preprint, arXiv:1909.05805, 2019.
  3. A. Garber, A. Magazinov, Voronoi conjecture for five-dimensional parallelohedra, preprint, arXiv:1906.05193, 2019.
  4. M. Dutour-Sikirić, A. Garber, A. Magazinov, On the Voronoi Conjecture for combinatorially Voronoi parallelohedra in dimension five, preprint, arXiv:1812.02964, 2018.
  5. M. Dutour-Sikirić, A. Garber, On periodic triangulations of Zn, preprint, arXiv:1810.10911, 2018.
  6. A. Garber, On triangular paperfolding patterns, preprint, arXiv:1807.05627, 2018.
  7. A. Garber, On Helly number for crystals and cut-and-project sets, preprint, arXiv:1605.07881, 2016, accepted to Contemporary Mathematics.
  8. D. Frettlöh, A. Garber, Bounded distance and bilipschitz equivalence of Delone sets, preprint, available at the web-page of Dirk Frettlöh.

Refereed journal publications

  1. A. Garber, E. Roldán-Pensado, On a Helly-type question for central symmetry, Periodica Mathematica Hungarica, 79:1 (2019), 78--85, DOI:10.1007/s10998-018-0263-y.
  2. D. Frettlöh, A. Garber, Weighted 1×1 cut-and-project sets in bounded distance to a lattice, Discrete & Computational Geometry, 64:3 (2019), 649--661, DOI:10.1007/s00454-018-0005-1.
  3. I. A. Baburin, M. Bouniaev, N. Dolbilin, N. Yu. Erokhovets, A. Garber, S. V. Krivovichev, E. Schulte, On the Origin of Crystallinity: a Lower Bound for the Regularity Radius of Delone Sets, Acta Crystallographica Section A, A74:6 (2018), 616--629, DOI:10.1107/S2053273318012135.
  4. D. Frettlöh, A. Garber, Pisot substitution sequences, one dimensional cut-and-project sets and bounded remainder sets with fractal boundary, Indagationes Mathematicae, 29:4 (2018), 1114--1130, DOI:10.1016/j.indag.2018.05.012.
  5. A. Garber, On π-surfaces of four-dimensional parallelohedra, Annals of Combinatorics, 21:4 (2017), 551--572, DOI:10.1007/s00026-017-0366-9
  6. M. Dutour-Sikirić, A. Garber, A. Schürmann, C. Waldmann, The complete classification of five-dimensional Dirichlet-Voronoi polyhedra of translational lattices, Acta Crystallographica A72 (2016), 673--683, DOI:10.1107/S2053273316011682.
  7. D. Frettlöh, A. Garber, Symmetries of Monocoronal Tilings, Discrete Mathematics & Theoretical Computer Science, 17:2 (2015), 203--234, the paper is available at the journal's web-site .
  8. A. Balitskiy, A. Garber, R. Karasev, Another ham sandwich in the plane, Annals of Combinatorics, 19:2 (2015), DOI:10.1007/s00026-015-0270-0.
  9. A. Garber, A. Gavrilyuk, A. Magazinov, The Voronoi conjecture for parallelohedra with simply connected δ-surface, Discrete & Computational Geometry, 53:2 (2015), DOI:10.1007/s00454-014-9660-z.
  10. A. Garber, Belt diameter of Π-zonotopes, European Journal of Combinatorics, 34:5 (2013), 923--933. DOI:10.1016/j.ejc.2013.01.005.
  11. A.I. Garber, Belt distance between facets of space-filling zonotopes, Mathematical Notes, 92:3-4 (2012), 345--355. DOI:10.1134/S0001434612090064.
  12. A. Garber, The second Voronoi conjecture on parallelohedra for zonotopes, Moscow Journal of Combinatorics and Number Theory, 1:2 (2011), 113--119. The paper on MJCNT web-site.
  13. A.I. Garber, On equivalence classes of separated nets (in Russian), Modeling and Analysis of Information Systems, 16:2 (2009), 109--118. The paper on MathNet web-site.
  14. A.I. Garber, Graphs of linear operators, Proceedings of the Steklov Institute of Mathematics, 263 (2008), 57--64. DOI:10.1134/S0081543808040056.
  15. A.I. Garber, Graph of difference operator for p-ary sequences, Functional Analysis and Other Mathematics, 1:2 (2006), 159--173. DOI:10.1007/s11853-007-0011-y.

Non-refereed publications and proceedings

  1. A.I. Garber, Complicated sequences due to V.I. Arnold (in Russian), Materials of the 9th International Seminar “Discrete Mathematics and its Applications” devoted to 75th Anniversary of the academician O.B. Lupanov, 2007, 374--376.
  2. A.I. Garber, A.P. Poyarkov, On permutahedra (in Russian), Vestnik MGU, ser. 1, iss. 2 (2006), 3--8.
  3. A.I. Garber, A.A. Glazyrin, Rigidity of some classes of cubillages, Proceedings of Second COE Workshop on Sphere Packings, May 30 - June 5, 2005, pp. 86--89.
  4. A.I. Garber, A.P. Poyarkov, On permutahedra, Voronoi's Impact in Modern Science. Book 3: Proceedings of Voronoi Conference on analytic number theory and spatial tesselations, Kyiv, Institute of Mathematics, 2005, pp. 137--145.
Grants and awards

Grants and awards

  • 2020-present. Alexander von Humboldt Foundation Fellowship for experienced researchers.
  • 2018-present. SQuaREs program “Delone Sets: Local Rules in Crystalline Structures” at American Institute of Mathematics, San Jose, CA.
  • 2016-2018. NSF Conference grant DMS-1623600, co-PI.
  • 2014. “Dynasty” Foundation grant for young mathematicians.
  • October-December, 2013. Winner of joint DAAD (German Academic Exchange Service) and Moscow State University Scholarships Program “Vladimir Vernadskii” for joint research in Germany.
  • 2011-2013. Russian Federal Program “Kadry”. Co-PI of the project 16.740.11.0568 “Functional Analysis and Discrete Geometry”.
  • 2011-2013. Participation in Russian Government “Megagrant” program in the project 11.G34.31.0053 as research fellow of Delone Laboratory of Discrete and Computational Geometry.
  • 2010-2014. Russian Government Program for the Support of Leading Scientific Schools (grants ??-5413.2010.1 and ??-4995-2012.1, member of research team).
  • 2008-2014. Participation in several research projects funded by the Russian Foundation for Basic Research. RFBR grants 08-01-00565 (project in 2008-2010, member of research team), 08-01-91202 (joint Russian-Japanese RFBR-JSPS project in 2008-2009, member of research team), 11-01-00633 (project in 2011-2013, member of research team), 11-01-00735 (project in 2011-2013, member of research team).
Visiting researcher
  • February 23 - March 9, 2006, Institute of Statistical Mathematics, Tokyo, Japan.
  • March 18 - April 1, 2009, Institute of Statistical Mathematics, Tokyo, Japan.
  • November 16 - December 12, 2009, Collaborative Research Center 701 of Bielefeld University, Bielefeld, Germany.
  • September 26 - October 31, 2010, Centre Interfacultaire Bernoulli, Ecole Polytechnique Federal de Lausanne, Switzerland.
  • September 29 - October 26, 2011, Queen's University, Kingston, ON, Canada.
  • September 25 - October 10, 2012, Queen's University, Kingston, ON, Canada.
  • October 30 - December 1, 2012, Collaborative Research Center 701 of Bielefeld University, Bielefeld, Germany.
  • October 15 - December 14, 2013, Research Center for Mathematical Modelling of Bielefeld University, Bielefeld, Germany.
  • January 6 - February 1, 2014, Collaborative Research Center 701 of Bielefeld University, Bielefeld, Germany.
  • May 5 - May 14, 2014, Rostock University, Rostock, Germany.
  • June 19 - July 2, 2016, Collaborative Research Center 701 of Bielefeld University, Bielefeld, Germany.
Selected presentations