Qualification:

• Mgr. - FPV UMB Banská Bystrica, 2007
• RNDr. - FPV UMB Banská Bystrica, 2007
• PhD. - FPV UMB Banská Bystrica, 2013
• Doc. - Mathematical Institute of the Silesian University in Opava, 2022

Science and research activities (2020 Mathematics Subject Classification):

• 37-XX Dynamical systems and ergodic theory

Selected publications:

1. M. Dirbák: Extensions of dynamical systems without increasing the entropy. Nonlinearity, vol. 21, 2008, pp. 2693-2713
2. M. Dirbák, P. Maličký: On the construction of non-invertible minimal skew products. J. Math. Anal. Appl., vol. 375, 2011, pp. 436-442.
3. M. Dirbák: Minimal skew products with hypertransitive or mixing propeties. Discrete Contin. Dyn. Syst., vol. 32, 2012, no. 5, pp. 1657-1674.
4. M. Dirbák, Ľ. Snoha, V. Špitalský, Minimality, transitivity, mixing and topological entropy on spaces with a free interval. Ergodic Theory Dynam. Systems, vol. 33, 2013, no. 6, pp. 1786-1812.
5. M. Dirbák, Minimal extensions of flows with amenable acting groups, Israel J. Math., vol. 207, 2015, no. 2, pp. 581-615.
6. M. Dirbák, R. Hric, P. Maličký, Ľ. Snoha, V. Špitalský, Minimality for actions of abelian semigroups on compact spaces with a free interval, Ergodic Theory Dynam. Systems 39 (2019), no. 11, 2968-2982.
7. M. Dirbák, First cohomology groups of minimal flows, Dissertationes Math. 562 (2021), 206 pp.
8. M. Dirbák, Ľ. Snoha, V. Špitalský: Minimal direct products, Trans. Amer. Math. Soc. 375 (2022), no. 9, 6453-6506.

Teaching activities: 

• Sequences and functions
• Discrete mathematics 2
• Linear algebra 2
• Measure and integral
• Set theory and metric spaces
• Functional analysis