Mgr. Jan Pavlík, Ph.D.
E-mail:   pavlik@fme.vutbr.cz 
Dept.:   Institute of Mathematics
Dept. of Algebra and Discrete Mathematics
Position:   Assistant Professor
Room:   A1/1944

Education and academic qualification

  • 2002, Mgr., Faculty of Natural Sciences at Masaryk University in Brně, specialization: Mathematics
  • 1997, - , Secondary Technical School of Chemistry, specialization: Analytical chemistry
  • 1992, - , Primary school Plovdivská, Brno

Career overview

  • 2005-present, assistent, Institute of Mathematics, Faculty of Mechanical Engineering, Brno University of Technology

Pedagogic activities

  • lectures within the PhD-studies at the Faculty of Natural Sciences of MU: practices of Foundations of mathematics, Linear algebra, Algebra

Scientific activities

  • Masters thesis: Morita Equivalence for the Ordered Structures

Non-University activities

  • 2000-present, member of committee of National Competition of High School Scientific Acitivity, specialization: Mathematics and Computer Science

Publications:

  • PAVLÍK, J.:
    On Reiterman Conversion, Laboratiire d'Informatique Fondamentale de Marseill
    conference proceedings
  • PAVLÍK, J.:
    Free algebras in varieties,
    Archivum Mathematicum, Vol.46, (2010), No.1, pp.25-38, ISSN 1212-5059, Masarykova univerzita
    journal article - other
  • PAVLÍK, J.:
    Varieties Defined without Colimits,
    Proceedings of the 7th Panhellenic Logic Symposium, pp.142-146, ISBN 978-960-530-108-8, (2009), Patras University Press
    conference paper
    akce: 7th Panhellenic Logic Symposium, Patras, 15.07.2009-19.07.2009
  • PAVLÍK, J.:
    Modules of Ordered Multiplicative Structures,
    Journal of Electrical Engineering , Vol.56, (2006), No.12/S, pp.73-76, ISSN 1335-3632, Slovak Centra of IEE
    journal article - other

List of publications at Portal BUT

Abstracts of most important papers:

  • PAVLÍK, J.:
    Free algebras in varieties,
    Archivum Mathematicum, Vol.46, (2010), No.1, pp.25-38, ISSN 1212-5059, Masarykova univerzita
    journal article - other
    We define varieties of algebras for an arbitrary endofunctor on a cocomplete category using pairs of natural transformations. This approach is proved to be equivalent to one of equational classes defined by equation arrows. Free algebras in the varieties are investigated and their existence is proved under the assumptions of accessibility.
  • PAVLÍK, J.:
    Varieties Defined without Colimits,
    Proceedings of the 7th Panhellenic Logic Symposium, pp.142-146, ISBN 978-960-530-108-8, (2009), Patras University Press
    conference paper
    akce: 7th Panhellenic Logic Symposium, Patras, 15.07.2009-19.07.2009
    We define polymeric varieties of algebras for a functor as an analogy of varieties of functor algebras on a cocomplete category and we show that these concepts are compatible. Every variety induced by a set of identities is then proved to be concretely isomorphic to a polymeric variety for some functor. Using the result we obtain an alternative description of Eilenberg-Moore category for a free monad.
  • PAVLÍK, J.:
    Modules of Ordered Multiplicative Structures,
    Journal of Electrical Engineering , Vol.56, (2006), No.12/S, pp.73-76, ISSN 1335-3632, Slovak Centra of IEE
    journal article - other
    In this paper we work with idempotent semirings called here ordered multiplicative structure (OM-structure). We study category of its modules. The aim of this work is to prepare field for further investigation of Morita equivalence of relevant structures.