Faculty of Mathematics, Physics
and Informatics
Comenius University Bratislava

Geometry and Topology

Doctoral Degree Program




full time / external

Usual duration:

full time form 4 years, external form 5 years

Language of courses:


Program director:

doc. RNDr. Pavel Chalmovianský, PhD.


doc. RNDr. Andrej Ferko, PhD.
doc. Mgr. Tibor Macko, PhD.
doc. RNDr. Jaroslav Guričan, CSc.
doc. RNDr. Martin Mačaj, PhD.

Related study programs: master's degree programs MathematicsComputer Graphics and Geometry

Description of the Study Program

Geometry is one of the oldest sciences. It is a mathematical disciplin which models and investigates the space in the most general sense, the geometric forms in space as such and also in their mutual relations. It is also a basic means for application of mathematics, an invaluable tool for realization of algorithms and construction of models of space-objects and scenes in computer graphics. The meaning of topology (general, algebraic and differential), having as global characteristics the investigation and use of the idea of continuity in the framework of mathematics, consists in exact description of the notions originally intuitively understood, in a unifying look at the grounds of many mathematical disciplines, theoretical physics, as well as many diverse geometrical constructions. The applied geometry is a basis for geometric modelling, computer-assisted design (CAGD) and for technical and economical calculations in the technological preparations of production. Many disciplines of applied geometry are presently considered as parts of computer graphics. From the needs of computer graphics, an important role is played also by discrete, algebraic and differential geometry. They are, of course, especially important also on their own.

What to Expect

The study program is a set of subjects and a set of rules compiled in such a way that successful completion of the subjects while maintaining the above rules allows the student to obtain a university degree. For each study program, a recommended study plan is set, which is compiled so that by completing it, the student meets the conditions for successful completion of studies within its standard length. The creation of a study plan is usually based on a modular (block) principle to enable students to continuously adjust the focus within the chosen field of study and expand the scope of study. The study plan is divided into compulsory, optional and elective subjects. The subject consists of individual independent educational activities or their combination, which are aimed at providing education in a defined area. The profile subjects of the study plan are compulsory or optional, and the student will acquire the knowledge and skills that are essential for the completion of the study program. The updating of study programs reflecting the development in the area is realized by selective subjects, which enable the use of short-term presence outside the faculty experts in the teaching process. The inclusion of several (selective) subjects in the programs is a response to the constructive comments of students and their interest in a particular area. The creation of the study plan considers the mission and goals set by the faculty in the field of science and research and in the field of education, which are stated in the Long-term plan of the faculty. The study program is prepared in accordance with the needs of practice and monitors the applicability of graduates. Graduates of the study program will obtain the 8th level of qualification according to the national qualification framework of the Slovak Republic. The study plan is prepared so that students can complete academic mobility abroad during their studies, as the faculty has concluded contracts with several partner universities that have related study programs.

Graduates' Career Opportunities

Graduates of the study program are employed mainly at universities and the Slovak Academy of Sciences, but also in companies. At present, every graduate has a reasonable job.

Employers rate program graduates as very capable in their positions, often focused on scientific or pedagogical work in the fields of geometry and topology, and applications for new graduates are regularly repeated (e.g. from the Department of Mathematics, Faculty of Mechanical Engineering, STU).

Doctoral Scholarships

Full-time doctoral students who have permanent residency in the European Union are entitled to receive a scholarship for the entire standard duration of their studies. The scholarships are paid starting on the date of enrollment. The scholarship is determined in accordance with the tables included in the Law no. 553/2003 Z.z. as follows: 

  • prior to completion of the qualification exam: 1025,50 EUR (6th class, 1st level)
  • after successful completion of the qualification exam: 1 194 EUR (7th class, 1st level)

Scholarships are not subject to taxes or other fees.

Doctoral studies are considered an equivalent to full time employment and in the majority of cases cannot be combined with another employment. Job holding applicants who intend to keep their job are advised to apply for the external (distance) form of doctoral studies. Doctoral students enrolled in the regular form are expected to participate in teaching activities such as conducting recitations or exam grading, in accordance with the needs of their corresponding departments.

List of Supervisors

prof. RNDr. Roman Ďurikovič, PhD.
doc. RNDr. Andrej Ferko, CSc.
doc. RNDr. Pavel Chalmovianský, PhD.
doc. RNDr. Demeter Krupka, DrSc. (La Trobe University, Melbourn a Palacký University Olomouc)
doc. Mgr. Tibor Macko, PhD.
prof. RNDr. Pavol Zlatoš, CSc.

Thesis Topics for Academic Year 2024/2025

  • Geometric methods of mixing optimization
    (supervisor: doc. RNDr. Pavel Chalmovianský, PhD.) 
  • Geometry and topology of smooth and topological manifolds and CW complexes
    (supervisor: doc. Mgr. Tibor Macko, PhD.)
  • Methods of creation nad visualization of 3D terrain models
    (supervisor: doc. RNDr. Andrej Ferko, PhD.)