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prof. RNDr. Josef Janyška, DSc.

Professor, Department of Mathematics and Statistics

Office: pav. 08/03025
Kotlářská 267/2
611 37 Brno

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Phone: +420 549 49 4660
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Basic information
CV

Curriculum vitae

Person Identification
  • Prof. RNDr. Josef Janyška, DSc
    born January 23, 1953, Lešná
    married, 2 children
Workplace
  • Faculty of Science
    Department of Mathematics and Statistics
    Kotlářská 2
    611 37 Brno
    Czech Republic
Employment Position
  • Professor
Education and Academic Qualifications
  • 1972-1977 study of mathematics and descriptive geometry at the Masaryk University in Brno
  • 1977 - the RNDr. thesis "Differential operators on the sphere"
  • 1984 - the CSc. degree (PhD) - thesis "Geometric prolongation functors and natural operations with connections"
  • 1988 - Associated Professor
  • 1996 - the habilitation - thesis "Some natural operations in general relativistic theories"
  • 2007 - DSc. thesis "Natural operators and their applications"
  • 2007 - Professor
Employment Summary
  • 1977 - 80 Assistant at the Department of Algebra and Geometry, Faculty of Science, Masaryk University, Brno
  • 1980 - 85 Assistant Professor at the Department of Algebra and Geometry, Faculty of Science, Masaryk University, Brno
  • 1985 - 88 Assistant Professor at the Department of Mathematics, Faculty of Science, Masaryk University, Brno
  • 1988 - 2006 Associated Professor at the Department of Mathematics, Faculty of Science, Masaryk University, Brno
  • 2007 Professor at the Department of Mathematics and Statistics, Faculty of Science, Masaryk University, Brno
Pedagogical Activities
  • Analytical geometry, descriptive geometry, history of geometry.
  • MSc. Thesis supervised in geometry and descriptive geometry
  • PhD. Thesis supervised in differential geometry and history of geometry.
Scientific and Research Activities
  • The main area of my research is differential geometry. The most important contributions deal with classification of natural operators of certain types and applications of differential geometric methods in theoretical physics. At present, I am mainly interested in geometrical models of general relativistic quantum mechanics.
Academical Stays
  • 1983 - Leningrad State University (2 months) and Moskow State University (3 months) - studying stay.
  • 1998 - University of Florence (3 months) - studying stay.
  • 1991 - University of Florence (3 months) - studying stay.
  • 1993 - University of Florence (4 months) - studying stay.
  • 1995 - University of Florence (1 month).
  • 1996 - University of Florence (1 month).
  • 1997 - University of Florence (1 month).
  • 1998 - University of Florence (2 months).
  • 1999 - University of Florence (1 month).
  • 2000 - University of Florence (1 month).
  • 2001 - University of Florence (1 month).
  • 2002 - University of Florence (6 weeks).
  • 2003 - University of Florence (5 weeks).
  • 2004 - University of Florence (1 month).
  • 2005 - University of Florence (1 month).
  • 2006 - University of Florence (2 months).
  • 2007 - University of Florence (2 weeks).
  • 2009 - University of Florence (1 month).
University Activities
  • Member of the Internal Evaluation Council of MU, since 2016.
  • Member of the Commission for Information Technology of MU, since 2012.
  • Member of the Economic Commission of MU, since 2010.
  • Member of the Scientific Council of MU, 2012 - 2019.
  • Vice rector of MU, 2012 - 2015.
  • Member of the Scientific Council of the Faculty of Sciences MU, 2010 - 2018.
  • Vice dean of the Faculty of Sciences MU, 2010 - 2012.
  • Head of Mathematical Section of the Faculty of Sciences MU, 2000 - 2007.
  • Member of the Academic Senate of the Faculty of Sciences MU, 1994-1999, head of the Academic Senate of the Faculty of Sciences MU, 1996-1999.
  • Member of the Academic Senate of the Masaryk University, 1996-2002. Vice head of the Academic Senate of the Masaryk University, 1999-2002
Extrauniversity Activities
  • Member of the American Mathematical Society.
  • Member of the Union of Czech Mathematicians and Physicists.
Appreciation of Science Community
  • Member of the Organizing Committees of international conferences Differential Geometry and Applications.
  • Editor of the Proceedings Diff. Geom. and Appl., World Scientific 1990 and Masaryk University 1996.
  • Managing editor of the mathematical journal Archivum Mathematicum, 1992-2000.
Selected Publications
  • JANYŠKA, Josef a Marco MODUGNO. Minimal coupling of gravitational and electromagnetic fields in General Relativity. In I. S. Krasil′shchik, A. B. Sossinsky, A. M. Verbovetsky. The Diverse World of PDEs : Geometry and Mathematical Physics. první. USA: American Mathematical Society, 2023, s. 151-164. ISBN 978-1-4704-7147-7. Dostupné z: https://dx.doi.org/10.1090/conm/788/15824. Odkaz na knihu. info
  • JANYŠKA, Josef a Marco MODUGNO. Smooth and F-smooth systems with applications to Covariant Quantum Mechanics. 1. vyd. Brno: MUNI Press, 2022, 128 s. Folia Facultatis Scientiarum Naturalium Universitatis Masarykianae Brunensia, Mathematica 20. ISBN 978-80-210-8626-5. Dostupné z: https://dx.doi.org/10.5817/CZ.MUNI.M210-8631-2022. URL info
  • JANYŠKA, Josef a Marco MODUGNO. An Introduction to Covariant Quantum Mechanics. 1. vyd. Berlin: Spriger Nature, 2022, 838 s. Fundamental Theories of Physics 205. ISBN 978-3-030-89588-4. Dostupné z: https://dx.doi.org/10.1007/978-3-030-89589-1. URL info
  • JANYŠKA, Josef, Jan VONDRA a Jiří HERBER. Analytická geometrie v rovině. 1. vydání, hybridní učebnice. Plzeň: Fraus, 2020, 72 s. Matematika s nadhledem od prváku k maturitě, 12. díl. ISBN 978-80-7489-529-6. URL info
  • JANYŠKA, Josef. Remarks on natural differential operators with tensor fields. Archivum Mathematicum. Brno: MU Brno, 2019, roč. 55, č. 5, s. 289-308. ISSN 0044-8753. Dostupné z: https://dx.doi.org/10.5817/AM2019-5-289. Full Text info
  • JANYŠKA, Josef. Remarks on local Lie algebras of pairs of functions. Czechoslovak Mathematical Journal. Praha: Institute of Mathematics, Czech Academy of Sciences, 2018, roč. 68 (2018), č. 3, s. 687-709. ISSN 0011-4642. Dostupné z: https://dx.doi.org/10.21136/CMJ.2017.0626-16. URL info
  • JANYŠKA, Josef, Marco MODUGNO a Dirk SALLER. Infinitesimal Symmetries in Covariant Quantum Mechanics. In Vladimír Dobrev. In book: Quantum Theory and Symmetries with Lie Theory and Its Applications in Physics, Volume 2. Německo: Springer-Verlag, 2018, s. 319-336. ISSN 2194-1009. Dostupné z: https://dx.doi.org/10.1007/978-981-13-2179-5_25. URL info
  • JANYŠKA, Josef a Marco MODUGNO. Quantum potential in covariant quantum mechanics. Differential Geometry and its Applications. Amsterdam: Elsevier Science, 2017, roč. 54, October, s. 175-193. ISSN 0926-2245. Dostupné z: https://dx.doi.org/10.1016/j.difgeo.2017.03.021. URL info
  • JANYŠKA, Josef. On Lie algebras of generators of infinitesimal symmetries of almost-cosymplectic-contact structures. Archivum Mathematicum. Brno: MU Brno, 2016, roč. 52, č. 5, s. 325-339. ISSN 1212-5059. Dostupné z: https://dx.doi.org/10.5817/AM2016-5-325. URL info
  • JANYŠKA, Josef. Remarks on infinitesimal symmetries of geometrical structures of the classical phase space of general relativistic test particle. International Journal of Geometrical Methods in Modern Physics. World Scientific, 2015, roč. 12, č. 8, s. "nestrankovano", 7 s. ISSN 0219-8878. Dostupné z: https://dx.doi.org/10.1142/S0219887815600208. URL info
  • JANYŠKA, Josef. Relations between constants of motion and conserved functions. Archivum Mathematicum. Brno: MU Brno, 2015, roč. 51, č. 5, s. 297-313. ISSN 0044-8753. Dostupné z: https://dx.doi.org/10.5817/AM2015-5-297. URL info
  • JANYŠKA, Josef. Special bracket versus Jacobi bracket on the classical phase space of general relativistic test particle. International Journal of Geometrical Methods in Modern Physics. World Scientific, 2014, roč. 11, č. 7, s. "nestrankovano", 31 s. ISSN 0219-8878. Dostupné z: https://dx.doi.org/10.1142/S0219887814600202. URL info
  • JANYŠKA, Josef. Hidden symmetries of the gravitational contact structure of the classical phase space of general relativistic test particle. Archivum Mathematicum. Brno: MU Brno, 2014, roč. 50, č. 5, s. 297-316. ISSN 0044-8753. Dostupné z: https://dx.doi.org/10.5817/AM2014-5-297. URL info
  • JANYŠKA, Josef. Analytická geometrie v prostoru. Fraus, 2014, 143 s. ISBN 978-80-7489-075-8. URL info
  • JANYŠKA, Josef a Martin MARKL. Combinatorial differential geometry and ideal Bianchi–Ricci identities II - the torsion case. Archivum Mathematicum. Brno: Masaryk University, 2012, roč. 48, č. 1, s. 61-80. ISSN 0044-8753. Dostupné z: https://dx.doi.org/10.5817/AM2012-1-61. URL info
  • JANYŠKA, Josef. Special phase functions and phase infinitesimal symmetries in classical general relativity. In Linan, M.B., Barbero, F., DeDiego, D.M. AIP Conf. Proc. 1460,, XX INTERNATIONAL FALL WORKSHOP ON GEOMETRY AND PHYSICS. 1. vyd. USA: American Institute of Physics, 2012, s. 135-140. ISBN 978-0-7354-1064-0. Dostupné z: https://dx.doi.org/10.1063/1.4733369. URL info
  • JANYŠKA, Josef a Raffaele VITOLO. On the characterization of infinitesimal symmetries of the relativistic phase space. Journal of Physics A: Mathematical and Theoretical. Velká Británie: IOP Publishing, 2012, roč. 45, č. 48, s. 1-28. ISSN 1751-8113. Dostupné z: https://dx.doi.org/10.1088/1751-8113/45/48/485205. URL info
  • JANYŠKA, Josef. Analytická geometrie: Kuželosečky. Fraus, 2012, 104 s. ISBN 978-80-7489-074-1. URL info
  • JANYŠKA, Josef. General covariant derivatives for general connections. Differential Geometry and its Applications. Elsevier, 2011, roč. 29, S1, s. "S116"-"S124", 9 s. ISSN 0926-2245. Dostupné z: https://dx.doi.org/10.1016/j.difgeo.2011.04.016. URL info
  • JANYŠKA, Josef a Martin MARKL. Combinatorial differential geometry and ideal Bianchi–Ricci identities. Advances in Geometry. de Gruyter, 2011, roč. 11, č. 3, s. 509-540. ISSN 1615-715X. Dostupné z: https://dx.doi.org/10.1515/advgeom.2011.017. URL info
  • JANYŠKA, Josef. Reduction theorem for general connections. Annales Polonici Mathematici. Polsko, Varšava: Instytut Matematyczny PAN, 2011, roč. 102, č. 3, s. 231-254. ISSN 0066-2216. Dostupné z: https://dx.doi.org/10.4064/ap102-3-4. URL info
  • JANYŠKA, Josef, Marco MODUGNO a Raffaele VITOLO. An algebraic approach to physical scales. Acta Applicandae Mathematicae. Kluwer, 2010, roč. 110, č. 3, s. 1249-1276. ISSN 0167-8019. URL info
  • JANYŠKA, Josef. Natural and gauge-natural bundles and natural Lagrangian structures. In Variations, Geometry and Physics. 1. vyd. New York: Nova Science Publishers, 2009, s. 143-166. in honour of Demeter Krupka's sixty-fifth birthday. ISBN 978-1-60456-920-9. URL info
  • JANYŠKA, Josef a Marco MODUGNO. Generalized geometrical structures of odd dimensional manifolds. Journal de Mathematiques Pures et Appliquees. Francie: Elsevier SAS, 2009, roč. 91, č. 2, s. 211-232. ISSN 0021-7824. URL URL info
  • JANYŠKA, Josef a Jan VONDRA. Natural principal connections on the principal gauge prolongation of a principal bundle. REPORTS ON MATHEMATICAL PHYSICS. Elsevier SAS, 2009, roč. 64, č. 3, s. 395-415. ISSN 0034-4877. URL info
  • JANYŠKA, Josef a Marco MODUGNO. Geometric structures of the classical general relativistic phase space. International Journal of Geometrical Methods in Modern Physics. World Scientific, 2008, roč. 5, č. 5, s. 699-754. ISSN 0219-8878. URL info
  • JANYŠKA, Josef. Higher order Utiyama's invariant interaction. REPORTS ON MATHEMATICAL PHYSICS. Elsevier SAS, 2007, roč. 59, č. 1, s. 63-81, 18 s. ISSN 0034-4877. URL info
  • JANYŠKA, Josef. Utiyama's reduction method and infinitesimal symmetries of invariant Lagrangians. In Symmetry and Preturbation Theory. první. Londýn: World Scientific, 2007, s. 255-256. ISBN 978-981-277-616-7. info
  • JANYŠKA, Josef a Marco MODUGNO. Graded Lie algebra of Hermitian tangent valued forms. Journal de Mathematiques Pures et Appliquees. Francie: Elsevier SAS, 2006, roč. 85, č. 5, s. 687-697. ISSN 0021-7824. URL info
  • JANYŠKA, Josef. Geometric structures on the tangent bundle of the Einstein spacetime. Archivum Mathematicum. Brno: Masaryk University, 2006, roč. 42, č. 2, s. 195-203. ISSN 0044-8753. URL info
  • JANYŠKA, Josef a Marco MODUGNO. Hermitian vector fields and special phase functions. International Journal of Geometrical Methods in Modern Physics. World Scientific, 2006, roč. 3, č. 4, s. 719-754. ISSN 0219-8878. URL info
  • JANYŠKA, Josef. Higher order Utiyama-like theorem. REPORTS ON MATHEMATICAL PHYSICS. Elsevier SAS, 2006, roč. 58, č. 1, s. 93-118. ISSN 0034-4877. URL info
  • JANYŠKA, Josef, Ivan KOLÁŘ a Antonela CABRAS. On the geometry of variational calculus on some functional bundles. Note di Matematica. Itálie: Univerzita Lecce, 2006, roč. 2006, č. 1, s. 51-66. ISSN 1123-2536. info
  • JANYŠKA, Josef a Marco MODUGNO. Quantum operators and Hermitian vector fields. In DIFFERENTIAL GEOMETRY AND PHYSICS. Čína: World Scientific, 2006, s. 97-106. ISBN 978-981-270-377-4. URL info
  • JANYŠKA, Josef a Marco MODUGNO. An outline of covariant quantum mechanics. In Recent Developments in Gravitational Phzsics. USA: Amazon, Institute of Physics Conference Series, 2006, s. 367-384. ISBN 978-0-7503-0943-1. URL info
  • JANYŠKA, Josef. Higher order valued reduction theorems for classical connections. Central European Journal of Mathematics. 2005, roč. 3, č. 2, s. 294-308. ISSN 1644-3616. URL info
  • JANYŠKA, Josef. Natural connections given by general linear and classical connections. In Differential Geometry and its Application. první. Praha: MATFYZ PRESS, 2005, s. 289-303. ISBN 80-86732-63-0. info
  • JANYŠKA, Josef. Reduction theorems for general linear connections. Differential Geometry and its Applications. Amsterdam: Elsevier Science, 2004, roč. 20, č. 2, s. 177-196. ISSN 0926-2245. info
  • JANYŠKA, Josef. On the curvature of tensor product connections and covariant differentials. Supplemento di Rendiconti del Circolo Matematico di Palermo. Palermo, 2004, roč. 72, č. 1, s. 135-143. ISSN 0009-725X. info
  • JANYŠKA, Josef. Higher order valued reduction theorems for general linear connections. Note di Matematica. Itálie: Univerzita Lecce, 2004, roč. 23, č. 2, s. 75-97. ISSN 1123-2536. URL info
  • JANYŠKA, Josef, Ivan KOLÁŘ a Antonela CABRAS. Functorial prolongation of some functional bundles. Annales Academiae Paedagogicae Cracoviensis, Studia Mathematica IV. Krakov: Pedagogická akademie, 2004, roč. 2004, č. 1, s. 17-30. ISSN 1643-6555. info
  • JANYŠKA, Josef a Marco MODUGNO. Uniqueness results by covariance in covariant quantum mechanics. In Proceedings of the Second International Symposium on "Quantum Theory and Symmetries", eds. E. Kapuscik, A. Horzela. New Jersey - London - Singapore: World Scientific, 2002, s. 404-411. ISBN 981-02-4887-3. info
  • JANYŠKA, Josef a Marco MODUGNO. Covariant Schroedinger operator. J. Phys. A: Math. Gen. UK: Institute of Physics Publishing, 2002, roč. 35, č. 40, s. 8407-8434. ISSN 0305-4470. info
  • JANYŠKA, Josef a Marco MODUGNO. Covariant pre-quantum operators. In Proceedings of the International Conference on "Differential Geometry and Its Applications", eds. O. Kowalski, D. Krupka and J. Slovák. Opava: Silesian University, 2002, s. 285-308. ISBN 80-7248-166-5. info
  • JANYŠKA, Josef, Marco MODUGNO a Dirk SALLER. Covariant quantum mechanics and quantum symmetries. In Proceedings of the International Conference on "Recent Developments in General Relativity", eds. R. Cianci, R. Collina, M. Francaviglia and P. Fre. Německo: Springer-Verlag, 2002, s. 179-202. ISBN 80-7248-166-5. info
  • HORÁK, Pavel a Josef JANYŠKA. Analytická geometrie. 1. dotisk 1. vydání. Brno: Masarykova univerzita v Brně, 2002, 155 s. ISBN 80-210-1623-X. info
  • JANYŠKA, Josef. A remark on natural quantum Lagrangians and natural generalized Schroedinger operators in Galilei quantum mechanics. Supplemento ai Rendiconti del Circolo Matematico di Palermo,Serie II. Palermo, Itálie: Univerzita Palermo, 2001, roč. 66, č. 2, s. 117-128. ISSN 0009-725X. info
  • JANYŠKA, Josef. Natural vector fields and 2-vector fields on the tangent bundle of a pseudo-Riemannian manifold. Archivum Mathematicum. Brno: MU Brno, 2001, roč. 37, č. 2, s. 143-160. ISSN 0044-8753. URL info
  • JANYŠKA, Josef a Anna SEKANINOVÁ. Analytická teorie kuželoseček a kvadrik. 2. vyd. Brno: Masarykova univerzita, 2001, 178 s. ISBN 80-210-2604-9. info
  • JANYŠKA, Josef. Natural Poisson and Jacobi structures on the tangent bundle of a pseudo-Riemannian manifold. In Global Differential Geometry: The Mathematical Legacy of Alfred Gray. 1. vyd. USA: American Mathematical Society, 2001, s. 343-347. Contemporary Mathematics 288. ISBN 0-8218-2750-2. info
  • JANYŠKA, Josef a Marco MODUGNO. Quantisable functions in general relativity. 1. vyd. Ciombra: University of Coimbra, 2000, 21 s. Textos Mat. Ser. B. info
  • JANYŠKA, Josef a Marco MODUGNO. On the graded Lie algebra of quantisable forms. In Differential Geometry and Applications. 1. vyd. Brno: Masarykova Univerzita, 1999, s. 601-620. ISBN 80-210-2097-0. URL info
  • JANYŠKA, Josef, Arkadius JADCZYK a Marco MODUGNO. Galilei general relativistic quantum mechanics revisited. In Geometria, Física-Matemática e outros Ensaios. Coimbra: Univerzita Coimbra, 1998, s. 253-313. info
  • JANYŠKA, Josef a Ivan KOLÁŘ. Professor Karel Svoboda (1918 - 1997). Archivum Mathematicum. Brno: Masaryk University, 1998, roč. 1998, č. 2, s. i, 3 s. ISSN 0044-8753. URL info
  • JANYŠKA, Josef. Natural Lagrangians for quantum structures over 4-dimensional space-time. Rendiconti di Matematica, VII. Roma, 1998, roč. 18, č. 4, s. 623-648. ISSN 1120-7183. info
  • HORÁK, Pavel a Josef JANYŠKA. Analytická geometrie. Brno: Masarykova univerzita v Brně, 1997, 151 s. ISBN 80-210-1623-X. info
  • JANYŠKA, Josef a Marco MODUGNO. On quantum vector fields in general relativistic quantum mechanics. General Mathematics. Rumunsko, 1997, roč. 1997, č. 1, s. 199-217. ISSN 1221-5023. info
  • JANYŠKA, Josef a Anna SEKANINOVÁ. Analytická teorie kuželoseček a kvadrik. Vyd. 1. Brno: Masarykova univerzita, 1996, iii, 178. ISBN 8021014350. info
  • JANYŠKA, Josef. Natural symplectic stuctures on the tangent bundle of a space time. Supplemento ai Rendiconti del Circolo Matematico di Palermo,Serie II. 1996, roč. 43, č. 2, s. 153-162. ISSN 0009-725X. info
  • JANYŠKA, Josef a Marco MODUGNO. Classical particle phase space in general relativity. In Differential Geometry and Applications. Brno: Masarykova Univerzita, 1996, s. 573-602. ISBN 80-210-1369-9. URL info
  • JANYŠKA, Josef a Marco MODUGNO. Relations between linear connections on the tangent bundle and connections on the jet bundle of a fibred manifold. Archivum Mathematicum. Brno: MU Brno, 1996, roč. 32, č. 4, s. 281-288. ISSN 0044-8753. URL info
  • JANYŠKA, Josef. Remarks on symplectic and contact 2-forms in relativistic theories. Bollettino Unione Mat. Italiana (7). 1995, roč. 9-B, č. 4, s. 587-616. info
  • JANYŠKA, Josef. Natural quantum Lagrangians in Galilei quantum mechanics. Rendiconti di Matematica, VII. Roma, 1995, roč. 15, č. 4, s. 457-468. ISSN 1120-7183. info
  • Differential geometry and its applications :International conference on differential geometry and its applications Brno, Czechoslovakia 27 August - 2 September 1989. Edited by Josef Janyška - Demeter Krupka. Singapore: World Scientific, 1990, xiii, 465. ISBN 981-02-0188-5. info

2021/01/26

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