Faculty of Mathematics, Physics
and Informatics
Comenius University Bratislava

Theoretical and Mathematical Physics

Doctoral Degree Program




full time / external

Usual duration:

full time form 4 years, external form 5 years

Language of courses:


Program director:

prof. RNDr. Peter Moczo, DrSc.


doc. RNDr. Vladimír Balek, CSc.
doc. RNDr. Marián Fecko, PhD.
doc. RNDr. Tomáš Blažek, PhD.
doc. Mgr. Jozef Kristek, PhD.

Related study programs: master's degree programs Theoretical PhysicsPhysics of the Earth

Description of the Study Program

The graduate of the third degree of the university study program Theoretical Physics and Mathematical Physics masters an extensive mathematical apparatus and theoretical-physical methods for solving complex problems in the field of theoretical physics. The study enables the graduate to gain a detailed overview of a wide range of theoretical and mathematical methods in theoretical physics - the graduate has the opportunity to acquire advanced knowledge of theoretical physics focused on high-energy physics (formerly particle physics), geophysics, gravity and cosmology, non-relativistic quantum many-particle systems and mathematical physics, as well as related disciplines. He will also acquire deep theoretical and methodological knowledge of general physics, understand the connection with the experimental results of modern physics at the level of the current state of research in the world; they will learn the principles of individual and team scientific work, scientific research, scientific formulation of problems, they will learn to present scientific results. He is able to creatively apply the acquired knowledge in practice, acquires the ability to develop his own scientific discipline, finds employment in various fields of science, research, industry and services in the public and private sectors. The graduate will also acquire additional knowledge, skills and abilities: be able to prepare projects and submit them to grant agencies; is able to scientifically formulate research goals and provide solutions to complex problems in the field of theoretical physics; can lead teams of scientists, research and development workers; is able to follow the latest scientific and research trends in his field; is able to supplement and update their knowledge through lifelong learning; learn the principles of managerial work, leadership and control of team members; can design new physical ideas and process them mathematically. When designing methods and approaches, the graduate is aware of the ethical, legal and environmental aspects of the proposed solution to the problem and applies them in accordance with the principles of sustainable development.

What to Expect

Graduate of the study program theoretical physics and mathematical physics with a focus

  • on high-energy physics masters the latest knowledge about the structure of matter in the Universe and the methods of quantum field theory, on which the standard model of elementary particles is built. He participates in the research of possible extensions of the standard model, or related problems focused on particle physics, typically related to experiments on accelerators at CERN. In the case of deeper cooperation with CERN, he has extensive skills in modern shared programming and methods such as the Monte Carlo method.
  • on geophysics masters the scientific methods of physical research of the Earth and near space. Thanks to mathematical-physical and computer knowledge and methods, he is also able to participate in solving scientific problems of related disciplines that study structure and processes in the Earth. He masters the extensive mathematical apparatus of geophysical research, a modern programming language and basic optimization procedures to increase the computational efficiency of algorithms. He also masters methods of acquisition, processing and analysis of signal, image and large data sets, is able to develop new algorithms and computer programs, develop new methods of measuring and processing geophysical data.
  • on gravity and cosmology works or has experience in research projects in the field of relativity research and its extension, including black hole physics and quantum aspects of gravity, and in the study of universe. He has extensive experience with analytical and numerical solutions of complex mathematical problems. Can apply the latest knowledge in other theoretical areas of physics, including mathematical physics, to research the evolution of the universe and explain cosmological observations.
  • on mathematical physics masters formal approaches to the study of open problems of modern physics from the whole spectrum of particular physical areas. He is able not only to apply mathematical methods, but also to develop them and to propose new concepts for them in the areas of both theoretical, experimental and application. 
  • on non-relativistic quantum many-particle systems participates in the research of condensed matter, including phase transitions, with high variability of external conditions. He masters modern approaches designed to manage the complexity of many-particle systems and sophisticated mathematical methods for their solution. The graduate of each specialization is able to creatively apply the acquired knowledge in practice. Based on the acquired range of knowledge from mathematical-physical and computer methods, he is able to find application in other fields of science and research, in industry and services in the public and private sector.

Graduates' Career Opportunities

Graduates have found employment 

  1. in the academic sphere and basic research - FMFI UK in Bratislava, Earth Science Institute SAS (formerly Geophysical Institute SAS), Institute of Physics SAS, Institute of Experimental Physics SAS, abroad in CERN laboratory in Switzerland, at Charles University (Mathematical-Physical Faculty) in Prague, 
  2. in the Slovak Hydrometeorological Institute,
  3. in the ISC (International Seismological Center),
  4. in the CTBTO (Comprehensive Test Ban Treaty Organization), 
  5. in the development departments of private financial and banking institutions,
  6. in private companies focused on hazard and risk analysis (including geohazard and geo-risk), 
  7. in private software companies, 
  8. in other institutions (e.g. SvF STU, ÚSMH AV ČR) and companies.

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.

Thesis Topics for Academic Year 2024/2025

  • Effects of poroelasticity on earthquake motion
    (supervisor: prof. RNDr. Peter Moczo, DrSc.)
  • Underground structure anomaly identification using seismic waves
    (supervisor: doc. Mgr. Jozef Kristek, DrSc.)
  • Physically-consistent modelling of earthquake ruptures
    (supervisor: doc. Mgr. Martin Gális, PhD.)
  • 3Effects of the free-surface topography on earthquake ground motion and site effects of earthquakes
    (supervisor: prof. RNDr. Peter Moczo, DrSc.)
  • Resource efficient implementations of quantum protocols
    (supervisor: Mgr. Michal Sedlák, PhD.)
  • Geometry of Interactions Reviewed by Tensor Networks
    (supervisor: Mgr. Andrej Gendiar, PhD.)
  • Certification of performance of quantum devices
    (supervisor: doc. Mgr. Mário Ziman, PhD.)
  • Analysis of noncommutative field theories in matrix models formalism
    (supervisor: Mgr. Juraj Tekel, PhD.)
  • Analysis of noncommutative field theories in string modes formalism
    (supervisor: Mgr. Juraj Tekel, PhD.)
  • Phenomenological aspects of quantum space
    (supervisor: Mgr. Samuel Kováčik, PhD.)