prof. RNDr. Miroslav Doupovec, CSc., dr. h. c.

E-mail:   doupovec@fme.vutbr.cz 
WWW:   http://www.mat.fme.vutbr.cz/home/doupovec
Dept.:   Institute of Mathematics
Dept. of Algebra and Discrete Mathematics
Position:   Professor
Room:   A1/1841
Phone:   +420 54114 2530

1951

Education and academic qualification

  • 1979-1984: study of mathematical analysis at the Masaryk University in Brno
  • 1984: the RNDr. degree, Masaryk University in Brno
  • 1988-1991: doctoral study, Mathematical Institute of the Czech Academy of Sciences
  • 1991: the CSc degree (Ph.D.) in geometry and topology, Charles University in Prague
  • 1998: the doc. degree (habilitation) in mathematics, Brno University of Technology, dissertation Some geometrical constructions in differential geometry
  • 2010: the prof. degree in applied mathematics, Brno University of Technology
  • 2012: dr. h. c., State Technical University, Izhevsk, Russia
  • 2017: dr. h. c., Technical University of Košice, Slovakia

Career overview

  • 1984: Tesla Brno, Assistant
  • 1984-1986: Šmeral Factory Brno, Computer analyst
  • since 1986: Faculty of Mechanical Engineering (FME), Brno University of Technology
  • 1986-1988: Lecturer, Brno University of Technology
  • 1988-1998: Assistant Professor, Brno University of Technology
  • 1998-2010: Associate Professor, Brno University of Technology
  • since 2010: Professor, Brno University of Technology

Pedagogic activities

  • BSC study programme: Mathematics, Numerical methods
  • MSC study programme, study branch Mathematical Engineering: Differential Geometry, Tensor Calculus
  • MSC Thesis supervised in differential geometry (including applications)
  • Ph.D. Thesis supervised in differential geometry

Scientific activities

  • Differential geometry and its applications.
  • Natural operators, connections, jets.
  • Prolongation of geometrical structures on fibered manifolds.

University activities

  • 02/2000-01/2006: Vice-dean for study courses, Faculty of Mechanical Engineering, Brno University of Technology
  • 02/2006-01/2014: Dean of Faculty of Mechanical Engineering
  • since 02/2014: vice-rector of Brno University of Technology for Studies and Student Affairs
  • since 2001: Member of the Scientific board of the Faculty of Mechanical Engineering, Brno University of Technology
  • since 03/2006: Member of the Scientific board of the Faculty of Science, Masaryk University in Brno
  • 03/2006: Member of the Scientific board of the Faculty of Mechanical Engineering, VŠB Technical University Ostrava
  • since 02/2007: Member of the Scientific board of the Faculty of Mechanical Engineering, Technical University Košice
  • 02/2010-01/2014: Member of the Scientific board of the Faculty of Mechanical Engineering, Technical University of Prague
  • since 04/2010: Member of the Scientific board of Brno University of Technology
  • 03/2011-01/2015: Member of the Scientific board of the Faculty of Mechanical Engineering, Technical University Bratislava
  • since 01/2013: Member of the Scientific board of the Faculty of Business and Management, Brno University of Technology
  • since 01/2013: Member of the Scientific board of Technical Museum in Brno

Prizing by scientific community

  • Reviewer for Mathematical Reviews.
  • Reviewer of Zentralblatt MATH.

Sum of citations (without self-citations) indexed within ISI Web of Knowledge

33

Sum of other citations (without self-citations)

80

Supervised courses:

Publications:

  • DOUPOVEC, M.; KUREK, J.; MIKULSKI, W.:
    Vertical functors on fibered manifolds,
    DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, Vol.54, (2017), No.A, pp.100-110, ISSN 0926-2245, ELSEVIER
    journal article
  • DOUPOVEC, M.; KUREŠ, M.:
    Some geometric constructions on Frobenius Weil bundles,
    DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, Vol.35, (2014), No.S, pp.143-149, ISSN 0926-2245, Elsevier
    journal article
  • DOUPOVEC, M.; MIKULSKI, W.:
    On symmetrization of higher order jets,
    Miskolc Mathematical Notes, Vol.14, (2013), No.2, pp.495-502, ISSN 1787-2405
    journal article
  • DOUPOVEC, M.; MIKULSKI, W.:
    On prolongation of higher order connections,
    Annales Polon.Math., Vol.102, (2011), No.3, pp.279-292, ISSN 0066-2216
    journal article
  • DOUPOVEC, M.; MIKULSKI, W.:
    On iteration of higher order jets and prolongation of connections,
    Annales Polon.Math., Vol.100, (2011), No.1, pp.55-75, ISSN 0066-2216
    journal article
  • DOUPOVEC, M.; KOLÁŘ, I.; MIKULSKI, W.:
    On the jets of foliation respecting maps,
    Czechoslovak Mathematical Journal, Vol.60, (2010), No.4, pp.951-960, ISSN 0011-4642
    journal article
  • DOUPOVEC, M.; MIKULSKI, W.:
    Reduction Theorems for Principal and Classical Connections,
    Acta Mathematica Sinica, Vol.26, (2010), No.1, pp.169-184, ISSN 1439-8516
    journal article

List of publications at Portal BUT

Abstracts of most important papers:

  • DOUPOVEC, M.; MIKULSKI, W.:
    On symmetrization of higher order jets,
    Miskolc Mathematical Notes, Vol.14, (2013), No.2, pp.495-502, ISSN 1787-2405
    journal article

    We discuss geometric constructions transforming r-th order semiholonomic or nonholonomic jets into holonomic ones.
  • DOUPOVEC, M.; MIKULSKI, W.:
    On prolongation of higher order connections,
    Annales Polon.Math., Vol.102, (2011), No.3, pp.279-292, ISSN 0066-2216
    journal article

    We describe all bundle functors G admitting natural operators transforming r-th order holonomic connections on a fibered manifold $Y\to M$ into r-th order holonomic connections on $GY\to M$. For second order holonomic connections we classify all such natural operators.
  • DOUPOVEC, M.; KOLÁŘ, I.; MIKULSKI, W.:
    On the jets of foliation respecting maps,
    Czechoslovak Mathematical Journal, Vol.60, (2010), No.4, pp.951-960, ISSN 0011-4642
    journal article

    Using Weil algabra techniques, we determine all finite dimensional homomorphic images of germs of foliation respecting maps.
  • DOUPOVEC, M.; MIKULSKI, W.:
    Reduction Theorems for Principal and Classical Connections,
    Acta Mathematica Sinica, Vol.26, (2010), No.1, pp.169-184, ISSN 1439-8516
    journal article

    We prove general reduction theorems for gauge natural operators transforming principal connections and classical linear connections on the base manifold into sections of an arbitrary gauge natural bundle. Then we apply our results to the principal prolongation of connections. Finally we describe all such gauge natural operators for some special cases of a Lie group G.
  • DOUPOVEC, M., KOLÁŘ, I.:
    Iteration of fiber product preserving bundle functors,
    Monatshefte fuer Mathematik, Vol.134, (2001), No.1, pp.39-50, ISSN 0026-9255
    journal article

    Using the theory of Weil algebras, we describe the composition of two product preserving bundle functors on the category of fibered manifolds with m-dimensional bases and fiber preserving maps with local diffeomorphisms as base maps. Then we deduce certain interesting geometric properties of the natural transformations of some of the iterated functors.