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 geometric tools (in particular those invented in the realm of Parabolic Geometries) to more practical problems in Neurogeometry, Medical Imaging, 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

A. Bansal, S. Kaushik, T. Bihonegn, D. Baručić, P.T. While, J. Slovák, Characterizing white matter multi-fiber structure using the Riemann-Finsler framework in HARDI, 2022, 12pp.
S. Kaushik, P. Kaushik, J. Slovak, Lenka Zajickova, Two-phase image analysis approach to compute the diameter of nanomaterials, 2020, 24pp.

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

    2023

  1. Bundles of Weyl structures and invariant calculus for parabolic geometries
    CAP, and Jan SLOVÁK, Bundles of Weyl structures and invariant calculus for parabolic geometries, Contemp. Math., 788, American Mathematical Society, Providence, RI, 2023, 53–72. ISBN: 978-1-4704-7147-7
  2. Automatic Tractography and Segmentation using Finsler Geometry based on Higher-order Tensor Fields
    Avinash BANSAL, Sumit KAUSHIK, BIHONEGN, Temesgen Tsegaye, and SLOVÁK, Jan, Automatic Tractography and Segmentation using Finsler Geometry based on Higher-order Tensor Fields. Computer Methods and Programs in Biomedicine. Elsevier, 240 (2023), 107630, 18 pp. ISSN 0169-2607. DOI10.1016/j.cmpb.2023.107630

    3. 2022

  3. Non-holonomic equations for the normal extremals in geometric control theory
    GOVER, A. Rod, a Jan SLOVÁK, Non-holonomic equations for the normal extremals in geometric control theory, Journal of Geometry and Physics, 171 (2022), 104395.

    4. 2021

  4. Geodesic ray-tracing in white matter fiber crossing region using decomposition of 4th order tensor
    BANSAL, Avinash , KAUSHIK, Sumit, BIHONEGN, Temesgen Tsegaye, SLOVÁK, Jan, Geodesic ray-tracing in white matter fiber crossing region using decomposition of 4th order tensor Proceedings Volume 12088, 17th International Symposium on Medical Information Processing and Analysis; 120880Q (2021), Campinas, Brazil https://doi.org/10.1117/12.2606129
  5. Geodesic Fiber Tracking in White Matter using Activation Function
    BIHONEGN, Temesgen Tsegaye, Sumit KAUSHIK, Avinash BANSAL, Lubomír VOJTÍŠEK a SLOVÁK, Jan, Geodesic fiber tracking in white matter using activation function. Computer Methods and Programs in Biomedicine. Elsevier, 208 (2021), 106283, 14 pp. ISSN 0169-2607. doi:10.1016/j.cmpb.2021.106283.
  6. Notes on Tractor Calculi
    SLOVAK, Jan, SUCHANEK, Radek, Notes on Tractor Calculi, Chapter in the book Differential Geometry, Differential Equations, and Mathematical Physics The Wisła 19 Summer School, Ulan, Maria, Schneider, Eivind (Eds.), Springer, Birkhauser, 2021, ISBN 978-3-030-63252-6, 37pp.
  7. Potential biomarkers from positive definite 4th order tensors in HARDI
    KAUSHIK, Sumit, Jan KYBIC, Avinash, BANSAL, Temesgen Tsegaye BIHONEGN, Jan SLOVÁK .
    Potential biomarkers from positive definite 4th order tensors in HARDI, In 2021 IEEE 18th International Symposium on Biomedical Imaging (ISBI). New York: IEEE, 2021. s. 1003-1006. ISBN 978-1-6654-1246-9. doi:10.1109/ISBI48211.2021.9434144.
  8. Subriemannian metrics and the metrizability of parabolic geometries
    CALDERBANK, David M.J., SLOVÁK, Jan, SOUCEK, Vladimir, Subriemannian metrics and the metrizability of parabolic geometries, Journal of Geometric Analysis, 31 (2021), 1671-1702. https://doi.org/10.1007/s12220-019-00320-1

    9. 2020

  9. 4th order tensors for multi-fiber resolution and segmentation in white matter
    BIHONEGN, Temesgen Tsegaye, BANSAL, Avinash , KAUSHIK, Sumit, Jan SLOVÁK .
    4th order tensors for multi-fiber resolution and segmentation in white matter, 7th International Conference on Biomedical and Bioinformatics Engineering (ICBBE ’20), November 06-09, 2020, Ritsumeikan University, Kyoto, Association for Computing Machinery, 36-42.
  10. Remark on bilinear operations on tensor fields
    SLOVÁK, Jan, Remark on bilinear operations on tensor fields, Archivum Mathematicum (Brno), 56, 5, 301-305.
  11. On the existence of local quaternionic contact geometries
    MINCHEV, Ivan, SLOVÁK, Jan, On the existence of local quaternionic contact geometries, New York J. Math. 26 (2020), 1093-1129.

    12. 2019

  12. HARDI segmentation via fourth order tensors and anisotropy preserving similarity measures
    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
  13. Lectures on Geometry of Monge–Ampère Equations with Maple
    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.
  14. Conformally Fedosov manifolds
    EASTWOOD, Michael, SLOVÁK, Jan, Conformally Fedosov manifolds. Advances in Mathematics, 349 (2019), 839–868. doi:10.1016/j.aim.2019.04.004
  15. Constant Curvature Models in Sub-Riemannian Geometry
    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)

    16. 2018

  16. Calculus on symplectic manifolds.
    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
  17. DTI Segmentation using Anisotropy preserving Quaternion based Distance Measure
    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
  18. On the equivalence of quaternionic contact structures.
    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.

    19. 2015

  19. Research, Development and Higher Education - questions related to public governance
    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.
  20. Individualized on-line Education in STEM
    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.
  21. The Paradigm Change in STEM Education–Has It Happened Already?
    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.

    22. 2013

  22. Matematika drsně a svižně (Brisk Guide to Mathematics)
    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.

    23. 2012

  23. Free CR distributions
    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.

    24. 2010

  24. Inclusions between parabolic geometries
    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.

    25. 2009

  25. Parabolic Geometries I, Background and General Theory
    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.

    26. 2008

  26. Morphisms of almost product projective geometries
    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.

    27. 2006

  27. Generalized planar curves and quaternionic geometry
    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

  28. On distinguished curves in parabolic geometries
    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.
  29. Preferred parametrizations on homogeneous curves
    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.

    30. 2003

  30. Addendum to he geometry of hyperbolic and elliptic CR-manifolds of codimension two'
    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.
  31. Weyl structures for parabolic geometries
    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.

    32. 2002

  32. What Counts More: Rules or Intuition?
    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.

    33. 2001

  33. Bernstein-Gelfand-Gelfand sequences
    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.

    34. 2000

  34. Bernstein-Gelfand-Gelfand sequences
    SLOVÁK, Jan. Bernstein-Gelfand-Gelfand sequences. In International Conference on Lie Groups, Geometric Structures and Differential Equations. Kyoto: Kyoto University, 2000. p. 14-23.
  35. First order invariant differential operators for parabolic geometries
    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.
  36. Invariant operators on manifolds with almost Hermitian symmetric structures, III. Standard operators
    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.
  37. Non-standard invariant operators for quaternionic geometries
    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.
  38. Parabolic geometries and Bernstein-Gelfand-Gelfand sequences (Parabolic geometries and Bernstein-Gelfand-Gelfand sequences)
    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.
  39. The geometry of hyperbolic and elliptic CR-manifolds of codimension two
    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.

    40. 1999

  40. Invariant local twistor calculus for quaternionic structures and related geometries
    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.

    41. 1998

  41. Invariant operators and semi-holonomic Verma modules
    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.

    42. 1997

  42. Invariant operators on structures with almost Hermitian symmetric structures. I. Invariant differentiation.
    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.
  43. Invariant operators on structures with almost Hermitian symmmetric structures. II. Normal Cartan connections.
    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.
  44. Semiholonomic Verma modules (Semiholonomic Verma modules)
    SLOVÁK, Jan and Michael G. EASTWOOD. Semiholonomic Verma modules. Journal of Algebra, 1997, vol. 197, No 2, p. 424-448. ISSN 0021-8693.

    45. 1996

  45. On local flatness of manifolds with AHS-structures
    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.
  46. On the Geometry of Almost Hermitian Symmetric Structures
    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.
  47. Principal prolongations and geometries modeled on homogeneous spaces
    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.
  48. The Principal Prolongations of First Order G-structures
    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.

    49. 1995

  49. On multilinear operators commuting with Lie derivatives
    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.

    50. 1993

  50. Infinitesimally natural operators are natural
    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.
  51. Natural Operations in Differential Geometry
    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.
  52. Natural operators on conformal manifolds
    SLOVÁK, Jan. Natural operators on 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.

    53. Older papers

  53. Slovak, J., On invariant operations on a manifold with connection or metric, J. Differential Geometry, 1992, 36, 633-650
  54. 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
  55. Slovak, J, Bundle functors on fibred manifolds, Annals of Global Annal. and Geom., 9, 1991, 129-143
  56. 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
  57. 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
  58. Slovak, J., On natural connections on Riemannian manifolds, Comment. Math. Universitatis Carolinae, 30, 1989, 389-393
  59. Slovak, J. Peetre theorem for nonlinear operators , Annals of Global Annal. and Geom., 6, 1988, 273-283
  60. 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
  61. Slovak, J., On the finite order of some operators, Proceedings of the Conference on Differential Geometry and its Applications, 1986, Brno, 1987, 283-294
  62. 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
  63. Slovak, J., Smooth structures on fibre jet spaces, Czech. Math. Journal, 36, 1986, 358-375