A quick and detailed review of my publications and their impacts is seen at my Google Scholar page.

I am working in Geometric Analysis and I am mainly interested in analytic properties of operators with large groups of symmetries. This requires hard tools in classical Analysis, modern Differential Geometry, Representation Theory of Lie Groups and Lie algebras and many other algebraic and categorial tools.
Recently I have been also interested in applications of the general tools invented in the realm of Parabolic Geometries to more practical problems in Neurogeometry and Geometric Control Theory.
As a result of my innovative approach to courses, I have also been partly interested in psychological and technological aspects of teaching.
The most influential works are the two research monographs and the Annals of Mathematics article, see the years 2009, 2001, and 1993 below.

Not (yet) published recent works and preprints

S. Kaushik, J. Kybic, A. Bansal, T. Bihonegn, J. Slovák, Novel biomarkers from positive definite 4th order tensors in HARDI , 2020, 4pp.
T. Bihonegn, A. Bansal, S. Kaushik, J. Slovák, 4th order tensors for multi-fiber resolution and segmentation in white matter , 2020, 6pp. (accepted paper in 7th International Conference on Biomedical and Bioinformatics Engineering, November 06-09, 2020, Ritsumeikan University, Kyoto, Japan)
T. Bihonegn, S. Kaushik, A. Bansal, L. Vojtisek, J. Slovák, Geodesic Fiber Tracking in White Matter using Activation Function , 2020, 11pp.
J. Slovak, Remark on bilinear operations on tensor fields , 2020, 5pp.
J. Slovak, R. Suchanek, Notes on Tractor Calculi , 2020, 37pp.
A. Rod Gover, J. Slovak, Non-holonomic equations for the normal extremals in geometric control theory, arXiv:1909.06592, 2019, 20pp.

Other essential works (not published regularly)

M.G. Eastwood, J. Slovak, A primer to Q-curvature, 2001, 13pp.
J. Slovak, Parabolic Geometries , Research Lecture Notes, Adelaide, 1997, (used as part of DrSc dissertation, Brno, 1998), 70pp.
J. Slovak, Natural operators on conformal manifolds , Research Lecture Notes, University of Vienna, 1992 (used as habilitation thesis, Masaryk University, 1993), 138pp.

Published works

    2020

  1. MINCHEV, Ivan, SLOVÁK, Jan, On the existence of local quaternionic contact geometries, New York J. Math. 26 (2020), 1093-1129.
  2. 2019

  3. CALDERBANK, David M.J., SLOVÁK, Jan, SOUCEK, Vladimir, Subriemannian metrics and the metrizability of parabolic geometries, Journal of Geometric Analysis (2019), 32pp. https://doi.org/10.1007/s12220-019-00320-1
  4. KAUSHIK, Sumit , SLOVÁK, Jan, HARDI segmentation via fourth order tensors and anisotropy preserving similarity measures, Journal of Mathematical Imaging and Vision, October 2019, Volume 61, Issue 8, s. 1221–1234. https://doi.org/10.1007/s10851-019-00897-w
  5. KUSHNER, Alexei, LYCHAGIN, Valentin V., SLOVÁK, Jan, In R. Kycia et al. Nonlinear PDEs, Their Geometry, and Applications. Springer Nature, Birkhäuser, 2019. s. 53-94, 42 s. ISBN 978-3-030-17030-1, doi:10.1007/978-3-030-17031-8_2.
  6. EASTWOOD, Michael, SLOVÁK, Jan, Conformally Fedosov manifolds. Advances in Mathematics, 349 (2019), 839–868. doi:10.1016/j.aim.2019.04.004
  7. ALEKSEEVSKY, Dmitri, SLOVÁK, Jan, Medvedev, Alexandre, Constant Curvature Models in Sub-Riemannian Geometry . Journal of Geometry and Physics 138 (2019) 241–256. doi: 10.1016/j.geomphys.2018.09.013 (arXiv:1712.10278)
  8. 2018

  9. EASTWOOD, M.G., SLOVÁK, Jan. Calculus on symplectic manifolds. Archivum Mathematicum, vol. 54 (2018), issue 5, pp. 265-280. doi: 10.5817/AM2018-5-265
  10. S. KAUSHIK, SLOVÁK, Jan. DTI Segmentation using Anisotropy preserving Quaternion based Distance Measure. In: Campilho A., Karray F., ter Haar Romeny. (eds) Image Analysis and Recognition. ICIAR 2018. Lecture Notes in Computer Science, vol 10882, Springer (2018), 81-89. doi: 10.1007/978-3-319-93000-8_10
  11. Ivan MINCEV, SLOVÁK, Jan. On the equivalence of quaternionic contact structures. Annals of Global Analysis and Geometry, Vol. 53, 3 (2018), 331–375. Springer, 2017. ISSN 0232-704X. doi:10.1007/s10455-017-9580-2.
  12. 2015

  13. SLOVÁK, Jan. Research, Development and Higher Education - questions related to public governance. УПРАВЛЕНЧЕСКИЕ НАУКИ В СОВРЕМЕННОМ МИРЕ, Издательский дом Реальная экономика, (2015) 1, 649-654. ISSN 2412-2289.
  14. SLOVÁK, Jan. Individualized on-line Education in STEM. In Miroslav Hrubý. Distance Learning, Simulation and Communication. Brno: University of Defence, 2015. p. 120-126, 7 pp. ISBN 978-80-7231-992-3.
  15. SLOVÁK, Jan. The Paradigm Change in STEM Education–Has It Happened Already? In David Gibson, Jan Slovak. Building Sustainable R&D Centers in Emerging Technology Regions. Brno: Masaryk University, 2015. p. 177-188, 12 pp. ISBN 978-80-210-7855-0. doi:10.5817/CZ.MUNI.P210-7855-2015.
  16. 2013

  17. SLOVÁK, Jan, Martin PANÁK and Michal BULANT. Matematika drsně a svižně (Brisk Guide to Mathematics). 1. vyd. Brno: Masarykova univerzita, 2013. 773 pp. ISBN 978-80-210-6307-5. doi:10.5817/CZ.MUNI.O210-6308-2013.
  18. 2012

  19. SLOVÁK, Jan and Gerd SCHMALZ. Free CR distributions. Central European Journal of Mathematics, 2012, vol. 10, No 5, p. 1896-1913. ISSN 1895-1074. doi:10.2478/s11533-012-0090-y.
  20. 2010

  21. DOUBROV, Boris and Jan SLOVÁK. Inclusions between parabolic geometries. Pure and Applied Mathematics Quarterly, Boston: Int. Press, 2010, vol. 6, No 3, p. 755-780. ISSN 1558-8599.
  22. 2009

  23. SLOVÁK, Jan and Andreas CAP. Parabolic Geometries I, Background and General Theory. první. Providence, RI, USA: American Mathematical Society, 2009. 628 pp. Mathematical Surveys and Monographs, 154. ISBN 978-0-8218-2681-2.
  24. 2008

  25. HRDINA, Jaroslav and Jan SLOVÁK. Morphisms of almost product projective geometries. In Differential geometry and its applications. 2008. vyd. USA: World Scientific, 2008. p. 243-251, 9 pp. ISBN 978-981-279-060-6.
  26. 2006

  27. SLOVÁK, Jan and Jaroslav HRDINA. Generalized planar curves and quaternionic geometry. Annals of Global Analysis and Geometry, Springer, 2006, vol. 2006, No 29, p. 349-360. ISSN 0232-704X.
  28. 2004

  29. ČAP, Andreas, Jan SLOVÁK and Vojtěch ŽÁDNÍK. On distinguished curves in parabolic geometries. Transformation Groups, Boston: Birkhauser, 2004, vol. 9, No 2, p. 143-166. ISSN 1083-4362.
  30. SLOVÁK, Jan and Michael G. EASTWOOD. Preferred parametrizations on homogeneous curves. Commentationes mathematicae universitatis carolinae, Praha: Univerzita Karlova v Praze, 2004, vol. 45, No 4, p. 597-606. ISSN 0021-8693.
  31. 2003

  32. SLOVÁK, Jan and Gerd SCHMALZ. Addendum to he geometry of hyperbolic and elliptic CR-manifolds of codimension two' (Addendum to 'The geometry of hyperbolic and elliptic CR-manifolds of codimension two'). The Asian Journal of Mathematics, Boston: International Press, 2003, vol. 7, No 3, p. 303-306. ISSN 1093-6106.
  33. SLOVÁK, Jan and Andreas CAP. Weyl structures for parabolic geometries. Mathematica Scandinavica, Aarhus: Aarhus Universitet, 2003, vol. 93, No 1, p. 53-90. ISSN 0025-5521.
  34. 2002

  35. SLOVÁK, Jan. What Counts More: Rules or Intuition? Bach 2000. Music between Virgin Forest and Knowledge Society. (J. Fukac et al, eds.), Compostela Prize series, VUTIUM Press, 2002, 43-48. ISBN 84-607-5515-0.
  36. 2001

  37. SLOVÁK, Jan, Andreas CAP and Vladimír SOUČEK. Bernstein-Gelfand-Gelfand sequences. Annals of Mathematics, Princeton University: The Johns Hopkins University Press, 2001, vol. 154, No 1, p. 97-113. ISSN 0003-486X.
  38. 2000

  39. SLOVÁK, Jan. Bernstein-Gelfand-Gelfand sequences. In International Conference on Lie Groups, Geometric Structures and Differential Equations. Kyoto: Kyoto University, 2000. p. 14-23.
  40. SLOVÁK, Jan and Vladimír SOUČEK. First order invariant differential operators for parabolic geometries. In Seminaires & Congres. France: French Math. Soc., 2000. p. 249-273. ISBN 2-85629-094-9.
  41. SLOVÁK, Jan, Andreas CAP and Vladimír SOUČEK. Invariant operators on manifolds with almost Hermitian symmetric structures, III. Standard operators. Differential Geometry and its Applications, Amsterdam: Elsevier Science, 2000, vol. 12, No 1, p. 51-84. ISSN 0926-2245.
  42. SLOVÁK, Jan. Non-standard invariant operators for quaternionic geometries. In Proceedings, IIIrd International Workshop, Lie Theory and its Applications in Physics III. Singapore: World Scientific Publishing, 2000. p. 87-98. ISBN 981-02-4421-5.
  43. SLOVÁK, Jan. Parabolic geometries and Bernstein-Gelfand-Gelfand sequences. In Proceedings of the fourth international workshop on differential geometry. Brasov: Transilvania University Press, 2000. p. 261-266. ISBN 973-9474-68-3.
  44. SLOVÁK, Jan and Gerd SCHMALZ. The geometry of hyperbolic and elliptic CR-manifolds of codimension two. The Asian Journal of Mathematics, Boston: International Press, 2000, vol. 4, No 3, p. 565-598. ISSN 1093-6106.
  45. 1999

  46. SLOVÁK, Jan and A.R. GOVER. Invariant local twistor calculus for quaternionic structures and related geometries. Journal of Geometry and Physics, Amsterdam: Elsevier Science, 1999, vol. 32, No 1, p. 14-56. ISSN 0393-0440.
  47. 1998

  48. SLOVÁK, Jan. Invariant operators and semi-holonomic Verma modules. Singapore: World Scientific, 1998. 10 pp. Lie theory and its applications in physics II. ISBN 9810235399.
  49. 1997

  50. SLOVÁK, Jan, Andreas CAP and Vladimír SOUČEK. Invariant operators on structures with almost Hermitian symmetric structures. I. Invariant differentiation. Acta Math. Univ. Comenianae, 1997, vol. 66, No 1, p. 33-69. ISSN 0862-9544.
  51. SLOVÁK, Jan, Andreas CAP and Vladimír SOUČEK. Invariant operators on structures with almost Hermitian symmmetric structures. II. Normal Cartan connections. Acta Math. Univ. Comenianae, 1997, vol. 66, No 2, p. 203-220. ISSN 0862-9544.
  52. SLOVÁK, Jan and Michael G. EASTWOOD. Semiholonomic Verma modules. Journal of Algebra, 1997, vol. 197, No 2, p. 424-448. ISSN 0021-8693.
  53. 1996

  54. SLOVÁK, Jan and Andreas CAP. On local flatness of manifolds with AHS-structures. Supplemento ai Rendiconti del Circolo Matematico di Palermo,Serie II, Palermo, 1996, vol. 1996, No 43, p. 95-102. ISSN 0009-725X.
  55. SLOVÁK, Jan. On the Geometry of Almost Hermitian Symmetric Structures. In Differential Geometry and Applications Proceedings. Brno: Masarykova univerzita Brno, 1996. p. 191-206. ISBN 80-210-1369-9.
  56. SLOVÁK, Jan. Principal prolongations and geometries modeled on homogeneous spaces. Archivum Mathematicum, Brno: MU Brno, 1996, vol. 32, No 4, p. 325-342. ISSN 0044-8753.
  57. SLOVÁK, Jan. The Principal Prolongations of First Order G-structures. Supplemento ai Rendiconti del Circolo Matematico di Palermo,Serie II, 1996, vol. 1996, No 39, p. 123-131. ISSN 0009-725X.
  58. 1995

  59. SLOVÁK, Jan. On multilinear operators commuting with Lie derivatives. Annals of Global Analysis and Geometry, 1995, vol. 13, No 1, p. 251-279. ISSN 0232-704X.
  60. 1993

  61. SLOVÁK, Jan and A. CAP. Infinitesimally natural operators are natural. Differential Geometry and its Applications, 1993, vol. 2, No 1, p. 45-55. ISSN 0926-2245.
  62. KOLÁŘ, Ivan, Jan SLOVÁK and Peter W. MICHOR. Natural Operations in Differential Geometry. Berlin-Heidelberg-New York: Springer-Verlag, 1993. 434 pp. ISBN 3-540-56235-4.
  63. SLOVÁK, Jan. Natural operators a conformal manifolds. In Proceedings of the confer. on Differ.Geometry and its Appl. Opava: Silesian university, 1993. p. 335-349. ISBN 80-901581-0-2.
  64. Older papers

  65. Slovak, J., On invariant operations on a manifold with connection or metric, J. Differential Geometry, 1992, 36, 633-650
  66. Slovak, J., Invariant operators on pseudo-Riemannian manifolds, Comment. Math. Univ. Carolinae, 33, 269-276, 1992 Cap, A.; Slovak, J., Infinitesimally natural operators are natural, Differential Geometry and Its Applications, 2, 1992, 45-55
  67. Slovak, J, Bundle functors on fibred manifolds, Annals of Global Annal. and Geom., 9, 1991, 129-143
  68. Slovak, Jan, Actions of jet groups on manifolds, Proceedings of the Conference on Differential Geometry and its Applications, 1989, Brno, 1990, World Scientific, Singapure, 9pp
  69. Kolar, I.; Slovak, J., Prolongation of vector fields to jet bundles, Proceedings of the Winter School on Geometry and Physics, Srni 1989, Suppl. Rendiconti Circolo Mat. Palermo, Serie II, No 22, 103-111
  70. Slovak, J., On natural connections on Riemannian manifolds, Comment. Math. Universitatis Carolinae, 30, 1989, 389-393
  71. Slovak, J. Peetre theorem for nonlinear operators , Annals of Global Annal. and Geom., 6, 1988, 273-283
  72. Kolar, I; Slovak, J., On the geometric functors on manifolds , Proceedings of the Winter School on Geometry and Physics, Srni 1988, Suppl. Rendiconti Circolo Mat. Palermo, Serie II, No 21, 223-233
  73. Slovak, J., On the finite order of some operators, Proceedings of the Conference on Differential Geometry and its Applications, 1986, Brno, 1987, 283-294
  74. Slovak, J., Prolongations of connections and sprays with respect to Weil functors, Proceedings of the Winter School on Geometry and Physics, Srni 1987, Suppl. Rendiconti Circolo Mat. Palermo, Serie II, No 14, 143-155
  75. Slovak, J., Smooth structures on fibre jet spaces, Czech. Math. Journal, 36, 1986, 358-375