Applied Mathematics

Probability and Mathematical Statistics

Y Mgr. Markéta Zikmundová, PhD.
b marketa.zikmundova@vscht.cz
e +420220445032

Research is currently being pursued in three main directions. The first is the study of the stochastic differential equations in infinite dimension driven by a fractional Brownian motion and study of the stochastic partial differential equations (SPDE) with focus on (statistical) parameter estimation using the Stein method (possibly in combination with the Malliavin calculus). The SPDEs usually describe dynamical phenomenons (physical, chemical, biological etc.) significantly affected by random effects. Another field of research is the stochastic geometry and spatial statistics, which have many applications in image analysis and material research. Here we focus on the space (- time) models with interacting particles. The third field of interest is financial mathematics.

Discrete Mathematics

Y Jana Maxová
b maxovaj@vscht.cz
e +42022044 5039

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Our research group is mainly engaged in exploring open problems in combinatorics, discrete mathematics and graph theory in particular. In recent years, our group has dealt with classical topics of graph theory, such as various types of graph coloring (e.g. star coloring of bipartite graphs), applications of linear algebra in graph theory, graph minors, computational complexity of graph algorithms etc. Recently, our research focuses especially on the investigation of so-called cover-incomparability graphs (or shortly C-I graphs). These are recently defined graphs derived from a partially ordered sets such that two vertices are connected by an edge, if and only if these two points are either incomparable or one covers the other in the original ordered set. In this area, we have published several articles in journals that dealt with the recognition complexity and the structure of this newly defined class of graphs.

Dynamical Systems

Y Prof. RNDr. Drahoslava Janovská, CSc.
b janovskd@vscht.cz
e +42022044 5040

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Study of Dynamic Systems has a long tradition at UM. The first seminar, which dealt with the systems of differential equations and dynamical systems, was held at the department of mathematics already in 2002.
Currently we mainly
- focus on the study of discontinuous dynamical systems and their applications in biology, ecology and thermodynamics;
- investigate trajectories of discrete dynamical systems in particular applications;
- explore periodicity, quasiperiodicity, and the emergence of chaos in dynamic systems;
- develop and research methods to simulate falling films (stability, accuracy and applicability in industrial apparatuses).