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PhD study on MI, SAS

Information on doctorate study in academic year 2026/2027

Mathematical Institute of the Slovak Academy of Sciences in Bratislava (MI SAS, Bratislava) together with its branches:

  • Mathematical Institute, Košice (MI SAS Košice)
  • Department of Informatics in Bratislava (OI, Bratislava)
  • Institute of Mathematics and Informatics, Banská Bystrica (IMI, Banská Bystrica)

in cooperation Comenius University (UK, Bratislava), Slovak Technical University (STU, Bratislava), and Pavol Jozef Šafárik University (UPJŠ, Košice), opens doctoral study positions in the following fields:

  • Applied Mathematics (FMFI UK, Bratislava)
  • Mathematics (FMFI UK, Bratislava)
  • Informatics (FIIT STU, Bratislava)
  • Mathematics (PF UPJŠ, Košice)
  • Informatics (PF UPJŠ, Košice)

General information about doctoral studies at the given universities:

The standard length of full-time doctoral studies is 4 years, and 5 years for external studies. Full-time students receive a scholarship of 1 174,50 EUR (since January 1, 2026), which increases to 1 367,50 EUR (since January 1, 2026) after passing the doctoral exam. Additional funds are provided for travel expenses and rewards for excellent results.

Doctoral study topics and study programs:

Instructions for prospective students

To apply, send a message to mathinst@mat.savba.sk. The message must include the chosen supervisor and topic, along with the following documents:

  1. CV with a list of publications (if any)
  2. Motivation letter
  3. A copy of bachelor and master degree diploma (can be provided later if not yet available)
  4. Two academic recommendation letters, sent by the referee directly to mathinst@mat.savba.sk.

Formal applications are submitted at the respective university only after approval by the supervisor and provisional acceptance at our institute. Further admissions procedures follow the rules of the university.

Application deadlines

For application for study under respective study programs, contact us before the following dates:

  • FMFI UK: March 31, 2026
  • FIIT STU: -
  • PF UPJŠ: April 30, 2026

Dissertation topics in academic year 2026/2027

Applied Mathematics (FMFI UK)

  1. Quantum channels and higher order maps
    supervisor: Mgr. Anna Jenčová, DrSc., MI SAS, Bratislava,
    e-mail: anna.jencova@mat.savba.sk
    Annotation: Quantum channels describe the most general physically allowed transformations between quantum systems. The framework of higher order maps (HOMs) allows a more detailed study of general quantum protocols, such as channel measurements, channel transformations, channels with memory, etc. Nowadays, there is an increasing interest in understanding the structure and properties of HOMs. Possible goals of the proposed thesis include the study of the mathematical structure of HOMs from different points of view, like operator theory, category theory, linear algebra, or convex geometry. We will focus on nonclassical properties of HOMs, e.g. incompatibility or indefinite causal order, their classification, consequences and possible advantages in information processing.
  2. Aggregation on bounded lattices
    supervisor: Mgr. Andrea Zemánková, DrSc., MI SAS, Bratislava,
    e-mail: andrea.zemankova@mat.savba.sk
    Annotation: The aim of the work will be to investigate aggregation functions on lattices, to study the basic properties of aggregation and their modification required by applications. The expected outcome will be the results concerning the construction, characterization and representation of aggregation functions on lattices.

Mathematics (FMFI UK)

  1. Stability of boundary value problems for functional differential equations
    supervisor: Mgr. Natália Dilna, PhD., MI SAS, Bratislava,
    e-mail: natalia.dilna@mat.savba.sk
    Annotation: Functional differential equations constitute a class of differential equations with deviating arguments, typically involving delays or advances. The aim is to investigate selected stability properties of boundary value problems for these equations.
  2. Chromatic and flow problems in graph theory
    supervisor: RNDr. Martin Kochol, PhD., DSc., MI SAS, Bratislava,
    e-mail: martin.kochol@mat.savba.sk
    Annotation: Study of the smallest counterexamples for hypotheses of nowhere-zero flow problems, constructions of snarks and study relative problems by an agreement.
  3. Tutte polynomials and their generalizations
    supervisor: RNDr. Martin Kochol, PhD., DSc., MI SAS, Bratislava,
    e-mail: martin.kochol@mat.savba.sk
    Annotation: Study of generalizations of Tutte and characteristic polynomials with parameters for special classes of matroids.

Mathematics (PF UPJŠ)

  1. Schwarzschild metric and its generalization
    supervisor: doc. RNDr. Ján Brajerčík, PhD., MI SAS, Košice (external supervisor),
    e-mail: jan.brajercik@unipo.sk
    Annotation: The thesis deals with the mathematical foundations of the general relativity. The starting point is the structure of the Schwarzschild metric and the underlying geometric structures of the general relativity. The goal is to obtain assertions on the generalization of the Schwarzschild metric to metric dependent on velocities (Finsler metric) invariant to the action of the Lie groups of general relativity.

    References:

    • [1] De Felice, F.; Clarke, C.J.S. Relativity on Curved Manifolds. In Cambridge Monographs on Mathematical Physics; Cambridge University Press: Cambridge, UK, 1990.
    • [2] D. Krupka, Introduction to Global Variational Geometry, Atlantis Studies in Variational Geometry, D. Krupka, H. Sun (Eds.), Atlantis Press, 2015.
    • [3] D. Krupka, J. Brajerčík, Schwarzschild Spacetimes: Topology. Axioms 2022, 11 (12) 693. https://doi.org/10.3390/axioms11120693
  2. Differential invariants
    supervisor: doc. RNDr. Ján Brajerčík, PhD., MI SAS, Košice (external supervisor),
    e-mail: jan.brajercik@unipo.sk
    Annotation: The thesis is based on the theory of differential invariants contained in the publication [1]. A focus of the thesis are differential invariants of tensors. The thesis also deals with the basic consequences of invariance in global variational geometry, such as conservation laws for extremal equations. The goal is to find assertions on the structure of all differential invariants of the metric and the given tensor field. The obtained results can be used for finding invariant Lagrangians for different types of physical fields.

    References:

    • [1] D. Krupka, J. Janyška, Lectures on Differential Invariants, Folia Facultatis Scientiarum Naturalium Universitatis Purkynienae Brunensis, Mathematica 1, University J. E. Purkyně, Brno, 1990.
    • [2] D. Krupka, Introduction to Global Variational Geometry, Atlantis Studies in Variational Geometry, D. Krupka, H. Sun (Eds.), Atlantis Press, 2015.
    • [3] J. Brajerčík, Second order differential invariants of linear frames, Balkan J. Geom. Appl., Vol. 15, No. 2 (2010) 22-33 (electronic version).
  3. Qualitative properties of nonlinear functional differential equations
    supervisor: Ing. Irena Jadlovská, PhD., MI SAS, Košice,
    e-mail: jadlovska@saske.sk
    Annotation: The objective of this thesis is to study qualitative properties (asymptotic behavior, oscillation) of functional differential equations. The aim is to establish sharp criteria for broad classes of nonlinear equations with p-Laplacian-type operators.
  4. Classification of aggregation functions on ordered sets
    supervisor: RNDr. Jozef Pócs, PhD., MI SAS, Košice,
    e-mail: pocs@saske.sk
    Annotation: The objective of this work is the axiomatic study and analysis of aggregation functions defined on ordered sets. The aim is to classify these functions with regard to the algebraic properties of the structures on which they are defined and their possible applications in decision theory.
  5. Combinatorial properties of real lines
    supervisor: RNDr. Miroslav Repický, PhD., MI SAS, Košice,
    e-mail: repicky@saske.sk
    Annotation: The aim of the work is to study relational systems on the set of real numbers and their cardinal characteristics using methods of forcing, models of set theory, and descriptive set theory.

Informatics (PF UPJŠ)

  1. Complexity aspects of automata and formal languages
    supervisor: Ing. Michal Hospodár, PhD., MI SAS, Košice,
    e-mail: hospodar@saske.sk
    Annotation: In selected models of automata, we examine descriptional complexity of various language operations with additional requirements, such as membership in a specific language class or an upper bound on alphabet size. We also consider the computational complexity of some decision problems related to formal languages and automata.