## Doctoral Study – Mathematics

Degree: **Doctor, Ph.D.**

Standard Length of Study: **4 years**

Form of Study: **full-time / part-time**

Language: **Czech / English**

**Possibility of study internships abroad**

### DESCRIPTION

Doctoral study is a continuation of master study programmes guaranteed by the Department of Mathematics. The doctoral study programme is organized according to the scientific orientation of the Department. Applicants for admission to the Ph.D. programme can also have a Master is degree in mathematics or related study fields awarded by another university.

### WHAT WILL I LEARN?

Doctoral research topics are from the following areas:

- study of qualitative properties of nonlinear differential equations in one-dimensional and multi-dimensional cases,
- formulation of nonlinear mathematical models on time scales and their analysis,
- study of nonlinear eigenvalue problems, especially problems with degenerate and singular operators,
- bifurcations of solutions of nonlinear systems,
- effective methods of algebraic geometry for applications in geometric modelling; symbolic manipulations in computer-aided geometric design and symbolic-numerical computations,
- optimization of the choice of models of random variables in lifetime theory and regression analysis,
- study of properties of discrete structures (graphs, hypergraphs, matroids, codes); investigation of their mutual relations (colourings, homomorphisms) and the existence of special substructures (cycles, paths, factors),
- study of graph operators, especially graph closures, and related methods for the investigation of properties of graph structures,
- numerical analysis of problems of multi-phase flow and contact problems in biomechanics,
- development of new computational conservative schemes for numerical simulations in fluid mechanics.

### CAREER

Graduates demonstrate deep knowledge of advanced mathematical techniques in the fields of nonlinear differential equations, in the research of mathematical models on time scales, in the study of bifurcation of solutions in nonlinear systems, in the development of new methods for describing complex-shaped objects, in the optimalization of the choice of models of random variables in lifetime theory and regression analysis, in the study of the properties of discrete structures and graph operators, in the numerical analysis of problems in biomechanics, or in mathematics education, in methodology and educational psychology, and in historical and philosophical aspects of mathematics and education. Graduates will find jobs in applied and basic research, in the management of analysis groups and in the academic environment. Graduates will be able to work creatively in a chosen field in scientific and academic institutions and in the department of mathematics at some university.

doc. Ing. Bohumír Bastl, Ph.D. | Advanced symbo lic-numerical computations in geometry and geometrie modelling |

prof. RNDr. Miroslav Lávička, Ph.D. | Advanced symbo lic-numerical computations in geometry and geometrie modelling |

doc. RNDr. Jan Vršek, Ph.D. | Advanced symbo lic-numerical computations in geometry and geometrie modelling |

doc. RNDr. Jiří Benedikt, Ph.D. | Nonlinear boundary value problems for differential and difference equations |

doc. Ing. Radek Cibulka, Ph.D. | Nonlinear boundary value problems for differential and difference equations |

prof. RNDr. Pavel Drábek, DrSc. | Nonlinear boundary value problems for differential and difference equations |

prof. Ing. Petr Girg, Ph.D. | Nonlinear boundary value problems for differential and difference equations |

doc. Ing. Gabriela Holubová, Ph.D. | Nonlinear boundary value problems for differential and difference equations |

prof. RNDr. Milan Kučera, DrSc. | Nonlinear boundary value problems for differential and difference equations |

doc. RNDr. Petr Stehlík, Ph.D. | Nonlinear boundary value problems for differential and difference equations |

doc. Ing. Marek Brandner, Ph.D. | Numerical models, methods and algorithms: design and analysis |

doc. Ing. Josef Daněk, Ph.D. | Numerical models, methods and algorithms: design and analysis |

doc. Dr. Ing. Miroslav Rozložník, DSc. | Numerical models, methods and algorithms: design and analysis |

doc. RNDr. Tomáš Vejchodský, Ph.D. | Numerical models, methods and algorithms: design and analysis |

doc. Ing. Radek Cibulka, Ph.D. | Variational analysis and nonsmooth optimization algorithms |

doc. Ing. Roman Čada, Ph.D. | Algorithms for hard problems in combinatorial optimization |

doc. RNDr. Petr Stehlík, Ph.D. | Mathematical models of theoretical ecology |

prof. RNDr. Eduard Feireisl, DrSc. | Mathematical Models of Fluid Dynamics |

RNDr. Šárka Nečasová, Ph.D. | Mathematical Models of Fluid Dynamics |

doc. Ing. Roman Čada, Ph.D. | Structural graph theory |

doc. RNDr. Přemysl Holub, Ph.D. | Structural graph theory |

prof. RNDr. Tomáš Kaiser, DSc. | Structural graph theory |

prof. RNDr. Roman Nedela, DrSc. | Structural graph theory |

prof. RNDr. Zdeněk Ryjáček, DrSc. | Structural graph theory |

Ing. Petr Nečesal, Ph.D. | Nonlinear boundary value problems for differential and difference equations |

doc. Ing. Jan Pospíšil, Ph.D. | Nonlinear boundary value problems for differential and difference equations |

RNDr. Jan Papež, Ph.D. | Numerical models, methods and algorithms: design and analysis |

Ing. Jakub Šístek, Ph.D. | Numerical models, methods and algorithms: design and analysis |

Mgr. Ondřej Kreml, Ph.D. | Mathematical models of fluid dynamics |

RNDr. Mgr. Václav Mácha, Ph.D. | Mathematical models of fluid dynamics |

The list is updated based on the decision of the Dean, who appoints additional specialist consultants according to the supervisors' recommendations for specific students.