Alexey   Garber

Assistant Professor  

Office: BLHSB 2.518
Phone: (956) 882-6672

Dr. Alexey Garber

Dr. Garber is working on different problems of discrete geometry and combinatorics. His current research interests are parallelohedra theory (in particular, the Voronoi conjecture on parallelohedra), geometrical properties of quasicrystals (wobbling and bilipschitz equivalence to a lattice), and measures equipartitions.

Selected Publications

  • Dirk Frettlöh and Alexey Garber. "Pisot substitution sequences, one dimensional cut-and-project sets and bounded remainder sets with fractal boundary," Indagationes Mathematicae 29, no. 4 (August 2018): 1114-1130.

  • Alexey Garber. "On π-surfaces of four-dimensional parallelohedra," Annals of Combinatorics 21, no. 4 (December 2017): 551-572.

  • Mathieu Dutour Sikiric, Alexey Garber, Achill Schürmann, and Clara Waldmann. "The complete classification of five-dimensional Dirichlet–Voronoi polyhedra of translational lattices," Acta Crystallographica Section A 72, no. 6 (November 2016): 673–683.

  • Alexey Garber, Andrey Gavrilyuk, and Alexander Magazinov. "The Voronoi Conjecture for Parallelohedra with Simply Connected δ-Surfaces," Discrete & Computational Geometry 53, no. 2 (2015): 245–260.

  • Alexey Balitskiy, Alexey Garber, and Roman Karasev. "Another ham sandwich in the plane," Annals of Combinatorics 19, no. 2 (May 2015): 235–242.

  • Alexey Garber. "Graphs of linear operators," Proceedings of the Steklov Institute of Mathematics 263, no. 1 (2008): 57–64.

  • Igor Baburin, Mikhail Bouniaev, Nikolay Dolbilin, Nikolay Erokhovets, Alexey Garber, Sergey Krivovichev, and Egon Schulte. "On the Origin of Crystallinity: a Lower Bound for the Regularity Radius of Delone Sets," Acta Crystallographica Section A .

  • Alexey Garber. "On triangular paperfolding patterns," arXiv preprint arXiv:1807.05627 .

  • Alexey Garber and Edgardo Roldán-Pensado. "On a Helly-type question for central symmetry," Periodica Mathematica Hungarica .

  • Dirk Frettlöh and Alexey Garber. "Weighted 1x1 cut-and-project sets in bounded distance to a lattice," Discrete & Computational Geometry .

Selected Grants and Fellowships

  • Alexey Garber. Conferences on Discrete Geometry and Algebraic Combinatorics, National Science Foundation, $40,000.00 (2016 - 2018)

  • Nikolay Dolbilin. SQuaRE "Delaunay sets: local rules in crystalline structures", American Institute of Mathematics, San Jose, CA, (November 2018)

  • Alexey Garber. Dynasty Foundation Grant for Young Mathematicians, Dynasty Foundation, (January 2014 - August 2014)

  • Alexey Garber. researcher in the projects НШ-5413.2010.1 and НШ-4995-2012.1, Russian Government Program for the Support of Leading Scientific Schools, $62,500.00 (January 2010 - August 2014)

  • Alexey Garber. researcher in RFBR grants 08-01-00565, 08-01-91202, 11-01-00633, 11-01-00735, Russian Foundation for Basic Research, $198,000.00 (January 2008 - August 2014)

  • Alexey Garber. project 11.G34.31.0053 of the "Megagrant" program, research fellow of the Delone Laboratory of Discrete and Computational Geometry, Government of the Russian Federation, $4,867,500.00 (November 2011 - December 2013)

  • Alexey Garber. project 16.740.11.0568 "Functional Analysis and Discrete Geometry", Russian Federal Program "Kadry", $46,875.00 (January 2011 - December 2013)

Current Courses

MATH 2414 12 - Calculus II:
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MATH 4390 04 - Math Project:
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MATH 2412 14 - Precalculus:
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Previous Courses