PřF GEOT Geometry, Topology and Geometric Analysis
Name in Czech: Geometrie, topologie a geometrická analýza
doctoral full-time specialized
Included in the programme: PřF D-MA_ Mathematics and Statistics

Final state doctoral examination and defence of the doctoral thesis

Before submitting an application for the state doctoral exam, the doctoral candidate must have fulfilled all the obligations set out in the individual study plan to this milestone.

In particular, the student must have an agreed research project which is aimed at a dissertation and meets the quality standards of the program in this specialization. The Doctoral Board will select three of the following courses for the exam:

- Algebraic topology
- Application of analytic and geometric methods in other disciplines (both in mathematics and outside)
- Differential geometry of fibred manifolds
- Global Analysis
- Homological algebra
- Riemannian geometry
- Representations of Lie Groups and Algebras

The course of the discussion in the exam corresponds to the chosen focus of the dissertation. Students focusing on basic research will focus on advanced areas and contexts related to their own research; for dissertations aimed at more applied results, it may be the subject of discussion to verify mastering of the underlying foundations in a wider context.

Requirements of the study

The student has at least four semester subjects during the course of study outside of the dissertation's focus (5-15% of the total workload).
Upon agreement with the supervisor, a separate study will focus on broadening the knowledge of the given field and on the special parts required for the dissertation.

Research activities:
- Dissertation preparation - takes place during the whole study period and constitutes 60-70% of the workload
- Publishing activity - consists of at least one article in an impacted journal, accounts for 10-15% of the workload
- Pedagogical activities (participation in teaching) - Ph.D. student can take part in supervising bachelor's theses, conducting seminars, etc., up to a maximum of 150 hours per study (5-10% of the workload)
- Throughout the study, PhD students report on their project and results at international workshops and seminars (domestic and foreign), including international conferences. The expected extent of this activity is about 5-15% of the total workload
- Active participation in one of the specialized seminars at the Institute (5-10% of the workload)

Part of the study duties in the doctoral study program is the completion of a part of the study at a foreign institution of at least one month or another form of direct student participation in international cooperation.

The basic form of doctoral study is a full-time form. It is expected that if a student will properly fulfill all his / her duties, he / she will successfully complete his / her studies after four years of standard study period (he / she will present his / her application for defense and defend in the following period). The combined form should be used exceptionally, especially in cases where, for serious reasons, the student fails to finish his studies after 4 years, although he has properly fulfilled his duties within the ISP. The only task within the combined form is the work on the dissertation project.

Suggestion of theses topics and the topics of defended theses

-- Algorithmic construction of the Postnikov tower for diagrams of simplicial sets, Marek Filakovský (školitel Martin Čadek), https://is.muni.cz/auth/th/p82ai/?fakulta=1431

-- Geometric structures invariant to symmetries,
Jan Gregorovič (školitel Jan Slovák)
https://is.muni.cz/auth/th/pho8a/?fakulta=1431

-- Holonomie kvaternionickych kahlerovych variet,
Natalia Bezvitnaya (školitel Jan Slovák)
https://is.muni.cz/auth/th/j31y8/?fakulta=1431

-- Natural prolongation of principal connections,
Jan Vondra (školitel Josef Janyška)
https://is.muni.cz/th/szvqf/?so=nx

-- Symmetries of Parabolic Geometries,
Lenka Zalabová (školitel Jan Slovák)
https://is.muni.cz/th/phey4/?so=nx


Recommended progress through the study plan

Warning:

The study plan does not contain any courses.