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PhD study on MI, SAS

Information on doctorate study in academic year 2023/2024

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 2023/2024 in specialization

9–1–9 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 30, 2023.

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, 2023 (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 807.50,- EUR/per month before defending PhD. project and 940.50,- EUR/per month after defending PhD. project. Currently, no taxes are paid from awarded scholarship.

Dissertation topics in academic year 2023/2024

1. Algebraic structures motivated by many valued reasonings
   supervisor: Prof. Anatolij Dvurečenskij, MI SAS, Bratislava,
   e-mail: Please enable javascript to see e-mail addresses.
   Annotation: The aim is to analyze different algebraic structures like MV-algebras, extended MV-algebras, BL-algebras with their non-commutative generalizations and to study their basic characteristics like states and observables.
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. Qualitative theory of dynamic equations on time scales
   supervisor: Dr. Irena Jadlovská, MI SAS, Košice,
   e-mail: Please enable javascript to see e-mail addresses.
   Annotation: The aim is to study the qualitative properties (asymptotic behavior, the existence of nonoscillatory solutions, the zeros distribution, etc.) of solutions to systems of functional dynamic equations on time scales.
4. 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.
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. 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.
11. Aggregation on bounded lattices
    supervisor: Mgr. Andrea Zemánková, PhD, MI SAS, Bratislava,
    e-mail: Please enable javascript to see e-mail addresses.
    Annotation:

    The theory of aggregation focuses on the expression of complex data in a concise form, usually using a small group of representatives that best characterize the most important properties and structure of the given data, as working with the whole data set is usually very time-consuming and computationally demanding.

    The majority of well-known aggregation methods focus mainly on subsets of real numbers, most often on the unit interval. Recently, the need to work on more complex structures has emerged, as some applications do not allow the data to be transformed into chains of values and require the presence of incomparable values. Therefore, aggregation on lattices and partially ordered sets is currently in the center of attention, focusing mainly on the modification of classical and the design of new methods for aggregation on such structures.

    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. .