Faculty of Mathematics, Physics
and Informatics
Comenius University in Bratislava

Geometry and Topology

Doctoral Degree Program

Field:

Geometry and Topology

Form:

full time / external

Usual duration:

full time form 4 years, external form 5 years

Program director:

prof. RNDr. Július Korbaš, CSc.

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

Description of the Study Program

Geometry is one of the most ancient sciences. It is a mathematical discipline modeling and researching the space in the most general sense as well as geometric bodies in space and in their mutual relations. It is also a basic means for application of mathematics, invaluable tool for realization of algorithms and constructions of models of special objects and scenes in computer graphics. The meaning of topology (general, algebraic, differential), whose global characteristic is the research and exploitation of the idea of continuity in the framework of mathematics, lies in exact description of originally intuitively understood notions, in unifying look at bases of many mathematic disciplines, theoretical physics, as well as at various geometric constructions. Applied geometry is the starting point for geometric modelling, Computer Aided Geometric Design and for technical and economic calculations in the of technology of production. Many parts of applied geometry are nowadays seen as parts of computer graphics. Discrete, algebraic and differential geometry also constitute an important part of computer graphics.

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: 595,00 EUR (9th class, 1st level)
  • after successful completion of the qualification exam: 693,50 EUR (10th 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 2018/2019

  • Towards the light field manipulation and editting
    (supervisor: prof. RNDr. Roman Ďurikovič, PhD.)
  • The universal autonomous transport system ATS
    (supervisor: prof. RNDr. Roman Ďurikovič, PhD.)
  • Large scale simulations for multiple fluid dynamics with moving interfaces
    (supervisor: prof. RNDr. Roman Ďurikovič, PhD.)
  • Structure-aware synthesis an analysis for predictive appearance of surfaces with small 3D microstructures and printing spacially-varying reflectance for reproducing glossy materials
    (supervisor: prof. RNDr. Roman Ďurikovič, PhD.)
  • Subgraphs of multicriteria-optimized triangulations
    (supervisor: doc. RNDr. Andrej Ferko, CSc.)
  • Data-dependent, topology-preserving mesh simplification
    (supervisor: doc. RNDr. Andrej Ferko, CSc.)
  • Geometria a topológia hladkých variet a CW-komplexov
    (supervisor: prof. RNDr. Július Korbaš, CSc.)
  • Mathematical methods in subdivision methods and their convergence
    (supervisor: doc. RNDr. Pavel Chalmovianský, PhD.)
  • Application of Spherical Inversions in Problems of Euclidean and non-Euclidean Geometry
    (supervisor: doc. RNDr. Pavel Chalmoviansky, PhD.)
  • Methods of nonstandard analysis in topological groups
    (supervisor: prof. RNDr. Pavol Zlatoš, CSc.)
  • Methods of nonstandard analysis in harmonic analysis
    (supervisor: prof. RNDr. Pavol Zlatoš, CSc.)