Igor Zelenko
Professor
Education
- Ph.D. in Mathematics, Technion- Israel Institute of Technology, 2002,
- M.S. in Mathematics, Technion- Israel Institute of Technology, 1998
- B.S. in Mathematics, summa cum laude, Technion - Israel Institute of Technology, 1994
In the Profession
- 2024-present, Associate Head for Graduate Studies , Department of Mathematics, Texas
A&M University
- 2023-present, Professor, Department of Mathematics, Texas
A&M University
- 2015-2023, Associate Professor, Department of Mathematics, Texas
A&M University;
- 2008-2015, AssistantProfessor, Department of Mathematics, Texas
A&M University;
- 2005-2008, A long term Visiting Associate Professor at
International School for Advanced Studies (SISSA-ISAS), Trieste, Italy;
- 2002-2005, Research Associate at International School for Advanced Studies (SISSA-ISAS), Trieste, Italy.
Research or Scholarly Interests
Local differential geometry of nonholonomic structures of manifoilds,
including vector disributions, sub-Riemannian structures and CR
structure with application to Control theory, System theory, Robotics,
Neuroscience and transpoirtation problems, Gromov's h-principle for various types of vector distributions.
Major Awards
- Wolf prize for PhD students - Hebrew University, Jerusalem, 2001
Notable Recent Grants
- NSF Grant, ``Geometry and topology of nonholonomic
structures" (PI), Division of Mathematical Sciences (DMS), DMS 2105528,
award amount of \$235,306, March 1 2022- February 28, 2025.
- NSF Grant ``Geometry and Analysis on Nonholonomic structures on
Manifolds'', DMS 1406193, award amount of $130,188, September 1,
2014-August 31, 2017.
- Simons Foundation Collaboration Grant for Mathematicians,
number 524213, ``Geometry of nonholonomic structures on
manifolds", award amount of $42,000, September 1, 2017-August 31
2022.
- PI in NSF Grant ''Texas Geometry and Topology conference", DMS 2430866 (co-PIs Dean Baskin and Zhizhang Xie), award amount $97,614, November 2024-November 2027.
- co-PI
in NSF Grant ''Texas Geometry and Topology conference", DMS 1812040 (PI
J.M. Landsberg, co-PI Dean Baskin), award amount 90,000, May 1
2018-June 30 2024.
Seven Selected Publications or Scholarly Works
- G. Berkolaiko, I. Zelenko, Morse inequalities for ordered eigenvalues of generic self-adjoint families, Inventiones Mathematicae, publsihed online, https://doi.org/10.1007/s00222-024-01284-y, 48 pages.
- D. Sykes, I. Zelenko, On geometry of 2-nondegenerate CR structures of hypersurface type and flag structures on leaf spaces of Levi foliations, Advances in Mathematics, Volume 413, 2023,108850, ISSN 0001-8708, https://doi.org/10.1016/j.aim.2022.108850, 65 pages.
- C. Porter,I. Zelenko, Absolute parallelism for 2-nondegenerate CR structures via bigraded Tanaka prolongation, J. Reine Angew. Math. 777 (2021), 195--250.
- N. Hein, F. Sottile, I. Zelenko, A congruence modulo four for real Schubert calculus, J. Reine Angew. Math. 714 (2016), 151-174.
- B. Doubrov, I. Zelenko, On local geometry of non-holonomic rank 2 distributions, J. Lond. Math. Soc. (2) 80 (2009), no. 3, 545--566.
- I. Zelenko, C. Li, Differential geometry of curves in Lagrange Grassmannians with given Young diagram, Differential Geom. Appl. 27 (2009), no. 6, 723-742.
- I. Zelenko, M. Zhitomirskii, Rigid paths of generic 2-distributions on 3-manifolds, Duke Mathematical Journal, Vol. 79, no. 2, 1995, 281--307.
Recent Synergistic Activities
- Mentor for Research project for returning students of
Summer Mathematics Research Training High School (SMaRT) Camp at Texas
A&M University in June 2017.
- Organizer of weekly group graduate students meeting on
``Local Differential Geometry and sub-Riemannian geometry" since Fall
2019 at TAMU.
- The organizer of the Mathematical Tournament (Math
Wrangle) activity in Summer Mathematics Research Training High
School (SMaRT) Camp at Texas A&M University in 2012, 2013,2016,
and 2017.
- The writer and grader team leader for Power Team exam (2017, 2019)
and writer of various subject exams (2012, 2013, 2015, 2016, 2018) ,including
best student exam, for TAMU Math High School Contest;
- Lecturer at TAMUMath Circle, 2012, 2015, 2017, 2018, 2019.
Graduate Students and/or Postdocs
- Zaifeng Lin, Ph.D, graduated 2023 (Texas A&M University);
- David Sykes, Ph. D, graduated 2021 (Texas A&M University);
- Curtis Porter, Ph. D, graduated 2016 (Texas A&M University);
- Juan P. Gomez, Ph.D., graduated 2018 (Mechanical Engineering, Texas A&M University);
- Sofya Maslovskaya, Ph.D, graduated 2018 (ENSTA, Paris);
- Chengbo Li, Ph.D. , graduated 2009 (SISSA, Trieste, Italy);