Průchod studijním plánem

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.

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.