Lenka Zalabová

Education:
  • Master degree: Department of Mathematics and Statistics, Faculty of Science, Masaryk University, Brno (1997-2002).
    Study program: Pure mathematics, specialization: Discrete mathematics. Thesis: Invariant Objects on Homogeneous Spaces (in Czech).
  • Ph.D. degree: Department of Mathematics and Statistics, Faculty of Science, Masaryk University, Brno (2002-2007).
    Study program: Geometry, topology a global analysis, specialization: Geometrical structures on manifolds. Thesis: Symmetries of Parabolic Geometries.

    • Advisors:
  • Prof. Jan Slovák (Masaryk University),
  • Prof. Andreas Čap (University of Vienna).

    • Qualification:
  • Habilitation in Mathematics - geometry (2020). Details of the process can be found here (Masaryk University).

    • Postdocs:
  • The International Erwin Schroedinger Institute for Mathematical Physics, ESI Junior Fellowships program, Vienna, Austria (8/08-1/09)
  • Eduard Čech Center for Algebra and Geometry, Masaryk University and Academy of Sciences of the Czech Republic, Brno, Czech Republic (2/09-8/09)
  • Banach Center IMPAN , Warsaw, Poland (8/17-10/17)

    • International stays (selected):
  • 9/2024: Isaac Newton Institute for Mathematical Sciences, University of Cambridge, United Kingdom
  • 8/2023: Banff International Research Station for Mathematical Inovation and Discovery, Canada
  • 7/2018, 8/2019: Banach Center, Institute of Mathematics, Polish Academy of Sciences, Warsaw, Poland,
  • 8/2017 -- 10/2017: Banach Center, Institute of Mathematics, Polish Academy of Sciences, Simons Semester Stipend, Warsaw, Poland,
  • 7/2017: Department of Mathematical Sciences, Politecnico di Torino, Italy
  • 1/2016 -- 2/2016: Department of Mathematics and Statistics, University of Tromsø, Norway,
  • 9/2016: Department of Mathematical Sciences, Politecnico di Torino, Italy
  • 8/2015 -- 9/2015: Department of Mathematics and Statistics, University of Tromsø, Norway,
  • 9/2013: School of Mathematical Sciences, University of Adelaide, and Mathematical Sciences Institute, The Australian National University, Canberra, Australia,
  • 12/2012: Department of Mathematics, Aarhus University, Denmark,
  • 8/2008 -- 1/2009: The Erwin Schroedinger Institute for Mathematical Physics, Vienna, Austria.

    • Grants:
    Main Investigator:
  • GACR P201/11/P202: Symmetric and complete parabolic geometries
  • Norway Grants NF-CZ07-INP-4-121-2015: Symmetries of geometric structures (NF-CZ07-INP-4-2382015)
  • Norway Grants NF-CZ07-INP-5-258-2015: Submaximal set of transformations for parabolic geometries (NF-CZ07-INP-5-4362015)
    Member of the team:
  • GACR 24-10887S: Cartan supergeometries and Higher Cartan geometries
  • GACR 20-11473S: Symmetry and invariance in analysis, geometric modelling and control theory
  • GACR 17-01171S: Invariant differential operators and their applications in geometric modelling and control theory
  • GACR 201/05/H005: Algebra and Geometry: the reunion and trends in current mathematics
  • GACR 201/02/1390: Algebraic methods in geometric analysis and topology
  • MSMT LC505: Eduard Cech Center for Algebra and Geometry

    • Invited Lectures (selected):
  • 8/2023: Banff International Research Station for Mathematical Inovation and Discovery, Conformal geodesics, Banff, Canada, title Conformal geodesics and conserved quantities on conformally homogeneous spaces Canada
  • 7/2023: POLS Conference: Conformal and CR geometries, and applications, Warsaw, Poland, title First BGG operators on homogeneous parabolic geometries
    Publications:
  • L. Zalabová, Remarks on Symmetries of Parabolic Geometries, Archivum mathematicum, Vol. 42 (2006), Supplement, 357-368
  • L. Zalabová, Symmetries of almost Grassmannian Structures, Differential Geometry and its Applications, Proceedings of the 10th international conference, Olomouc (2007), 371-381
  • L. Zalabová, V. Žádník, Remarks on Grassmannian Symmetric Spaces, Archivum Mathematicum, Vol. 44 (2008), No. 5, 569-585
  • L. Zalabová, Symmetries of Parabolic Geometries, Differential Geometry and its Applications 27 (2009), No. 5, 605-622
  • L. Zalabová, Parabolic Symmetric Spaces, Annals of Global Analysis and Geometry, Vol. 37 (2010), Issue 2, 125-141
  • L. Zalabová, Symmetries of Parabolic Contact Structures, Journal of Geometry and Physics, Vol. 60 (2010), Issue 11 (November), 1698-1709
  • J. Gregorovič, L. Zalabová, Symmetric parabolic contact geometries and symmetric spaces, Transformation Groups 18 (2013), 711-737
  • L. Zalabová, A non--homogeneous, symmetric contact projective structure, Central European Journal of Mathematics, 2014, 12(6), 879-886
  • J. Gregorovič, L. Zalabová, On automorphisms with natural tangent action on homogeneous parabolic geometries, Journal of Lie Theory, Volume 25 (2015), 677-715
  • J. Gregorovič, L. Zalabová, Geometric properties of homogeneous parabolic geometries with generalized symmetries, Differential Geometry and its Applications, Volume 49, December 2016, 388–422
  • J. Gregorovič, L. Zalabová, Notes on symmetric conformal geometries, Archivum Mathematicum TOMUS 51/5, (2015), 287 - 296
  • J. Gregorovič, L. Zalabová, A construction of non--flat non--homogeneous symmetric parabolic geometries, Archivum Mathematicum, vol. 52 (2016), issue 5, 291-302
  • J. Gregorovič, L. Zalabová, Local generalized symmetries and locally symmetric parabolic geometries, SIGMA 13 (2017), 032, 33 pages
  • B. Kruglikov, H. Winther, L. Zalabová, Submaximally symmetric almost quaternionic structures, Transformation Groups 23 (2018), 723–741
  • J. Gregorovič, L. Zalabová, On symmetric CR geometries of hypersurface type, Journal of Geometric Analysis 29 (2019), 3135–3159
  • J. Hrdina, L. Zalabová, Local geometric control of a certain mechanism with the growth vector (4,7), Journal of Dynamical and Control Systems 26 (2020), 199–216
  • J. Hrdina, A. Návrat, L. Zalabová, Symmetries in geometric control theory using Maple, Mathematics and Computers in Simulation, Volume 190, 2021, Pages 474-493
  • J. Hrdina, A. Návrat, L. Zalabová, On symmetries of a sub--Riemannian structure with growth vector (4,7), Annali di Matematica (2022). https://doi.org/10.1007/s10231-022-01242-6
  • M. Eastwood, L. Zalabová, Special metrics and scales in parabolic geometry, Ann Glob Anal Geom (2022). https://doi.org/10.1007/s10455-022-09866-w
  • J. Gregorovič, L. Zalabová, First BGG operators on homogeneous conformal geometries, Class. Quantum Grav. 40 (2023) DOI 10.1088/1361-6382/acbc05
  • J. Gregorovič, L. Zalabová, First BGG operators via homogeneous examples, Journal of Geometry and Physics, Volume 192, October (2023)
  • J. Hrdina, A. Návrat, P. Vašík, L. Zalabová, Note on geometric algebras and control problems with SO(3)-symmetries, Mathematical Methods in the Applied Sciences, Volume 47, Issue 3, pp1257-1273 (2024)
    • Preprints:
  • J. Eisner, L Zalabová, Local control on quaternionic Heisenberg group of dimension 7, arXiv:2404.08953
  • J. Hrdina, A. Návrat, L. Zalabová, Geometric control theory of vertical rolling disc using symmetries, arXiv:1908.03352, preprint (extended version of Symmetries in geometric control theory using Maple published in MATCOM, includes Tanaka prolongation)
    • Teaching activities and lecture notes are available here (in Czech).
    Hlavní stránka