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PhD study on MI, SAS

Information on doctorate study in academic year 2024/2025

Mathematical institute, SAS (MI SAS, Bratislava) and its branches:

  • Mathematical Institute, Košice (MI SAS, Košice);
  • Department of Computer Science, Bratislava (DCS, Bratislava);
  • Institute of Mathematics and Computer Science MI SAS, Banská Bystrica (IMCS, Banská Bystrica)

in cooperation with Faculty of Mathematics, Physics and Informatics, Comenius University, Bratislava (FMPI CU, Bratislava) organizes PhD. study in academic year 2024/2025 in specialization

Applied mathematics.

Standard length of PhD study in internal form is 4 years and in external form 5 years.

Deadline for submitting applications is June 20, 2024 (date change).

In order to be able to attend PhD study, it is necessary to have university degree of at least second degree (equivalent of MSc. or similar).

Application form and required documents

In order to apply for the PhD study at MI SAS the following documents are required:

  • Filled application form (available only in Slovak :( )
    It can be filled for you, but the following information is necessary (can be sent via e-mail):
    • Citizenship (what country are you citizen of)
    • Name
    • Middle name, if available
    • Surname, if applicable also surname before marriage
    • Academic title
    • Marrital status
    • Date of birth: dd.mm.yyyy
    • Sex (M or F)
    • Place of birth (city and country of birth)
    • Country (current)
    • Nationality
    • ID number or passport number
    • Telephone contact
    • Email address
    • Current address (street, number, town, county/state, country, postal code)
    • Corresponding address, if differs from current address (street, number, town, county/state, country, postal code)
    • Chosen topic of PhD study (name, supervisor)
    • Finished university (name of university, department, start/end of study (mm/yyyy), academic title, study topic, study subject)
    • List of taken courses during university study (each semester) with exam results (A-F)
  • Curriculum vitae
  • Diploma/Degree or a document certifying finished second degree of university study (MSc., or equivalent)
  • List of publications (submitted/published), if available

Fees

There is no fee for enrolment into PhD study and for examination.

Examination

The examination for PhD study will be held in July, 2024 (precise date will be specified later, it depends on chosen topic) - examination questions are related to the topic of chosen topic of dissertation (in extent according to second degree of university study), language skill etc. Results will be examined be a designated committee (mostly consisting of other employees of MI, SAS).

The limit is to accept up to 3–5 internal PhD students and 3 external ones.

Scholarship amount: Scholarship awarded to PhD. students on Mathematical Institute, SAS is 1 025.50 EUR/per month before defending PhD. project and 1 194,- EUR/per month after defending PhD. project. Currently, no taxes are paid from awarded scholarship.

Dissertation topics in academic year 2024/2025

  1. Ulam-Hyers stability of the fractional functional differential equations
    supervisor: Natália Dilna, PhD., MI SAS, Bratislava,
    e-mail: Please enable javascript to see e-mail addresses.
    Annotation: Fractional differential calculus is an area of mathematical analysis that deals with derivatives of non-integer order. The interest in fractional differential calculus has increased in recent years due to its wide application in various fields. The goal is to investigate Ulam-Hyers' stability for fractional functional differential equations. This stability is a new type besides the well-known Lyapunov stability.
  2. Singular fractional differential equations
    supervisor: Prof. Michal Fečkan, MI SAS, Bratislava,
    e-mail: Please enable javascript to see e-mail addresses.
    Annotation: The aim is to study the existence of solutions for singularly perturbed systems of fractional differential equations.
  3. Relative entropies in quantum information theory
    supervisor: Anna Jenčová, DrSc., MI SAS, Bratislava,
    e-mail: Please enable javascript to see e-mail addresses.
    Annotation: Relative entropy is one of the fundamental concepts in information theory. These quantities describe operational characteristics of optimal procedures in various types of information-theoretic tasks, but also serve as an important mathematical tool. The class of quantum relative entropies is much richer than the classical counterpart and many of the possible quantities, their interpretations and mutual relations are not fully investigated. We focus on various versions of quantum Rényi relative entropies and their extensions, such as to infinite dimensions or for quantum channels, as well as their possible operational interpretations.
  4. Quantum channels and higher order maps
    supervisor: Anna Jenčová, DrSc., MI SAS, Bratislava,
    e-mail: Please enable javascript to see e-mail addresses.
    Annotation: Quantum channels describe 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.
  5. Algorithms for structural analysis of snarks
    supervisor: Assoc. Prof. Ján Karabáš, MI SAS, Banská Bystrica,
    e-mail: Please enable javascript to see e-mail addresses.
    Annotation: Main aim is to study and analyse state-of-art algorithms involved in structural analysis of snarks, find and implement new algorithms and use all of them in examination of all known and newly constructed snarks. Another important problem is related to characterisation and classification of known and newly found snarks with respect to specific set of invariants (the set could be extend if needed). The studied algorithms and the gathered data on snarks will serve in attacks to the open problems in the area.
  6. Chromatic and flow problems in graph theory
    supervisor: Martin Kochol, DSc., MI SAS, Bratislava,
    e-mail: Please enable javascript to see e-mail addresses.
    Annotation: Study of the smallest counterexamples for hypotheses of nowhere-zero flow problems, constructions of snarks and study relative problems by an agreement.
  7. Tutte polynomials and their generalizations
    supervisor: Martin Kochol, DSc., MI SAS, Bratislava,
    e-mail: Please enable javascript to see e-mail addresses.
    Annotation: Study of generalizations of Tutte and characteristic polynomials with parameters for special classes of matroids.
  8. Modern trends in aggregation theory
    supervisor: Assoc. Prof. Martin Papčo, MI SAS, Košice,
    e-mail: Please enable javascript to see e-mail addresses.
    Annotation: The goal is to investigate and to describe modern trends in aggregation theory, and to suggest their possible applications as well.
  9. Algebraic properties of aggregation functions
    supervisor: Dr. Jozef Pócs, MI SAS, Košice,
    e-mail: Please enable javascript to see e-mail addresses.
    Annotation: From the algebraic point of view aggregation functions form a clone. The aim of the dissertation is to investigate various properties of the mentioned clone using universal algebraic and lattice theoretic methods.
  10. Sparse symmetric graphs in machine learning
    supervisor: Assoc. Prof. Ondrej Šuch, IMCS, Banská Bystrica,
    e-mail: Please enable javascript to see e-mail addresses.
    Annotation: A popular approach to building complex classification models is to create an ensemble of simpler pairwise models. Combining pairwise models corresponds to a graph structure. Employing symmetric graphs allows us to prevent a potentially large prediction error, which occurs when a hard to distinguish class lacks sufficient coverage by a dense subset of the ensemble. The research topic combines deep neural networks, classical machine learning and theory of symmetric graphs (Cayley graphs).
  11. Derivation of coordinate system of three triangulation sensors
    supervisor: Prof. Gejza Wimmer, MI SAS, Bratislava,
    e-mail: Please enable javascript to see e-mail addresses.
    Annotation: The problem is to derive the coordinates of three laser sensors and the corresponding directions of their laser beams using measurements of a calibrated basic parallel scale.
  12. Aggregation on bounded lattices
    supervisor: Mgr. Andrea Zemánková, PhD, MI SAS, Bratislava,
    e-mail: Please enable javascript to see e-mail addresses.
    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.

PhD study usually starts on September, 1 unless specified otherwise.

For more information you can directly contact MI SAS, Bratislava.
Postal address: MI SAS, Štefánikova 49, Bratislava, SK-81473 Slovakia.
Phone number: +421 2 5249 7316 or +421 2 5751 0414.
E-mail: Please enable javascript to see e-mail addresses. .