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PhD study on MI, SAS

Information on doctorate study in academic year 2025/2026

Starting this year 2025 the process of admitting to a doctarate study is completely changed. Application date deadline is April 30, 2025 (due to some time for preparing details to your application, please contact your potential supervisor up to April 20, 2025 where in your e-mail communication you also use CC: anna.jencova at mat.savba.sk) and fee payments are mandatory for all applicants. Admission process will be held at Faculty on June 23, 2025. All students must be registered in AIS system. Even foreign students are registered to study in Slovak (even if it the language of study is different) in order to obtain a scholarship. (The process of applicaiton needs to be establisted via Slovak page for application!) Details are present at Faculty's page to a doctorate study:
https://fmph.uniba.sk/en/admissions/admissions-process/doctoral-degree-admissions/. Please contact your potential supervisor in order to communicate details of your application.

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 2025/2026 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 April 30, 2025.
(deadline for contact with your potential supervisor is April 20, 2025).

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). (For currently finishing students this can be sent later.)

Application form and required documents

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

• Filled application form in the English language.
• Copy of bachelor’s degree diploma (in English)
• Certified copy of master´s degree diploma (in English) – a student who has not yet completed his/her master’s degree study shall submit Official Confirmation of Study Towards University Degree (in English) - this can be sent later, if you are currently finishing your study.
• Official transcript of completed courses during the master’s study
• Internationally recognized English language certificate (copy); when applying for the English program
• Structured CV in English, signed, with higlighted achievements the applicant wishes to receive points for; as listed in the List of points awarded to applicants based on their previous achievements
• Copy of passport
• Two academic reference letters in English
• Motivation letter in English
• List of publications (submitted/published), if available
• The applicants will be required to prepare in collaboration with their potential adviser an Individual study plan (the form may be found at Tlačivá/Forms). This document allows the potential adviser to express his or her support for the application. It is therefore recommended that the applicants contact their chosen advisers prior to applying for their dissertation topic.

More details could be found at FMFI UK's page dedicated to doctorate study.

Examination

Examination will be according to rules stated by Comenius University:

After receiving your application, we will send you details of further steps in the admissions process, including the date and the form of the entrance examinations (if they are required).

At the end of the admissions process, you will receive an official decision letter about acceptance or rejection of your application at the address you have indicated in your application form. Typically, the results are available at the end of June.

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 2025/2026

1. 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.
2. 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.
3. 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.
4. 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.
5. 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.
6. 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.
7. 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.
8. 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.

1. Descriptional and computational complexity of formal languages
   supervisor: Dr. Galina Jirásková, MI SAS, Košice,
   e-mail: Please enable javascript to see e-mail addresses.
   Annotation: The aim is to get the descriptional and computational complexity of formal languages and operations on formal languages represented by various types of formal systems such as deterministic, nondeterministic, and alternating automata, regular expressions or context-free grammars. We focus on the trade-offs between different models of formal systems, as well as on the complexity of language operations with arguments that satisfy some special properties.
2. Recurrent families of discrete probability distributions in collective risk models
   supervisor: Assoc. Prof. Ján Mačutek, MI SAS, Bratislava,
   e-mail: Please enable javascript to see e-mail addresses.
   consultant: Gábor Szűcs, PhD. (FMFI UK)
   Annotation: The disseration thesis will focus on analyses of recurrent families of discrete probability distributions which are used in actuarial science. The topic is important, because the new directive Solvency II changed several aspects which substantially affected computations and methodology of insurance companies. The crucial task of insurance companies is the best possible estimation of the number of insured events, of insurance claims, and of tech-nical reserves. The thesis will concentrate mainly on theoretical research in probablity and mathematical modelling, but it will address also some practical applications of actuarial science.
3. Classes of penalty and other functions in the 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 study the position and the classes of penalty and other functions use in aggregation theory, and, in the corresponding framework, to suggest their possible applications as well.
4. 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 methods.

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. .