doc. RNDr. Martin Kolář, Ph.D.
Consultant
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Doctoral degree in full-time or combined form. The language of instruction is Czech.
The programme can be studied only as a single subject with a specialization (Algebra, Number Theory and Mathematical Logic, General Mathematics, Geometry, Topology and Geometric Analysis, Mathematical Analysis or Probability, Statistics and Mathematical Modelling).
The aim of the program is to prepare high-quality scientific specialists in the fields covered by the Institute of Mathematics and Statistics at MU. Graduates should be prepared primarily for further scientific work in academic institutions, but also for possible application in practice. Upon graduation, graduates who wish to continue their research work are motivated to gain long-term foreign experience as post-doctoral students.
The individual research teams of the Institute of Mathematics and Statistics cover the following research themes in which PhD students are also trained:
Attention is also paid to the preparation for pedagogical work at universities. The study is based on an individual study plan and is completed by a state doctoral examination and a defense of doctoral dissertation. In addition to Czech, English is also the working language of the program.
Practical training is not a mandatory part of this program.
Graduates will apply to mathematical workplaces of basic research, universities and scientific research institutes of the Academy of Sciences of the Czech Republic.
The best graduates are fully prepared to successfully apply for postdoctoral positions at high-quality universities abroad.
Graduates can also act as college teachers at universities with a technical, economic and pedagogical focus.
Graduates of applied specializations will also find use in practice, in institutions where the use of deterministic and stochastic models of real processes where specialized statistical software is being developed, and in institutions focusing on research in the field of probabilistic and mathematical-statistical methods.
Data from the previous admission procedure (1 Jan – 30 Apr 2022)
More information about admission process for international applicants in general can be found here.
Date of the entrance exam
The applicants will receive information about the entrance exam via e-mail usually at least 10 days before the exam.
Please, always check your e-mails, including spam folders.
Conditions of admission
A total of at least 80 points is required for admission.
Successful applicants are informed of their acceptance via e-mail and subsequently receive an invitation to the enrolment.
Programme capacity
The capacity of a given programme is not fixed; students are admitted based on a decision by the Doctoral Board after assessing their aptitude for study and motivation.
In the single-subject studies, the student deepens knowledge in the concrete focus of the degree programme and chooses one specialization. The specialization is stated in the university diploma.
The main theme is devoted to the study of abelian extensions of the field of rational numbers, possibly of an imaginary quadratic field. The attention is focused on objects related to the ideal class groups (e.g., the group of circular units, Stickelberger ideal, the group of elliptic units).
Examples of some older dissertations: https://is.muni.cz/th/mwiet/?lang=en or https://is.muni.cz/th/jbpxt/?lang=en or https://is.muni.cz/th/atke4/?lang=en
Accessible categories and their applications in algebra, model theory and homotopy theory. For example: Abstract elementary classes, Accessible model categories.
My publications: https://arxiv.org/find/grp_math/1/au:+rosicky/0/1/0/all/0/1?skip=0&query_id=8094c174213ee61e
OBJECTIVES: The research deals with connections of algebra with logic, in particular quantum, tense, and fuzzy. The basic tool are residuated posets, enriched categories, and orthogonal structures but the emphasis is also on quantales in connection with C*-algebras and noncommutative geometry. The practical part of the research is oriented to simulation and validation of value streams using formal words, trees, and categorical concepts. We study algebraic methods for aggregation of processes and their effects, in particular in a probabilistic environment.
AIM: a) For example, one of our research goals is a characterization of the basic quantum-physical model by means of automorphisms of its underlying orthogonality space.
b) The theoretical aspects of aggregation of multidimensional data, rankings, relations and strings will be developed in more detail, especially connected to practical situations. The mathematical model is designed primarily for industrial planning but could be used for a wider range of applications (bioinformatics etc.).
My publications:
https://www.muni.cz/en/people/1197-jan-paseka/publications
Enriched category theory provides one of the ways in which we can capture higher-dimensional categories. For instance, 2-categories, as studied by the Australian school, are enriched categories. Recently, the subject of (infinity,1)-categories, aka quasicategories, has been developed by Joyal and Lurie amongst others and Riehl and Verity have shown that these can also be captured using enriched category theory. There are many open questions and problems to be explored in this area, which involves a rich mixture of homotopy theory, enriched category theory and categorical universal algebra.
The modern theory of finite semigroups links universal algebra and topology with the theory of formal languages and logic in theoretical computer science. The main motivation of that research is decidability of concatenation hierarchies of regular languages. The algebraic objects in the centre of our interest are the lattice of pseudovarieties of finite ordered semigroups and the free profinite semigroups in these pseudovarieties.
FOCUS:Doctoral research project may focus on the theory of varieties of regular languages or on the theory of profinite semigroups. However, there are also other questions combining theoretical computer science and algebra, for example questions concerning computational complexity of identity checking problem for a fixed finite semigroup.
EXAMPLES of potential doctoral projects:- The equational characterizations of pseudovarieties,
- Completeness of the equational logic for psedovarieties of finite algebras,
- Concatenation hierarchies of star-free languages,
- Computational complexity of basic problems for finite semigroups.
My publications: http://www.math.muni.cz/~klima/Math/publications.html
Přímkové plochy představují klasické téma s bohatou historií, zajímavými souvislostmi a slibnou budoucností. Cílem práce je shromáždit, přiblížit a rozvinout některá ze zmiňovaných hledisek. Od kandidáta se předpokládá trpělivost při studiu literatury (často starší a cizojazyčné) a tvůrčí přístup při výběru a zpracování nabytých poznatků.
Uspořádané algebraické struktury tvoří jedny z nejvíce studovaných struktur v algebře. Pozornost je věnována hlavně problematice 19. a 20. století a speciálně české matematice; nejsou však opomíjeny ani biografické a bibliografické aspekty.
PŘEDPOKLADY: Pro výzkum bude potřebná alespoň rámcová orientace v teori osobnostních typů, např. původní teorie Junga a indikátory Myersové-Briggsové (viz https://cs.wikipedia.org/wiki/Myers-Briggs_Type_Indicator) a přiměřená znalost statistických metod pro vyhodnocování šetření.
V případě zájmu kontaktujte přímo Jana Slováka na slovak@muni.cz.
PROJECT EXAMPLES
PROJECT EXAMPLES:
RESEARCH AREA:
Complex analysis in several variables leads naturally to geometric problems concerning boundaries of domains, and more generally real submanifolds of the complex space (so called CR manifolds). One of the main objectives is to understand symmetries of such manifolds and invariants with respect to holomorphic transformations.
PROJECT EXAMPLES:
Differential equations with argument deviations are important for applied science and arise frequently in population dynamics, epidemiology, economy (in particular, as models of capital growth) and many other fields. Models of various real dynamical phenomena are frequently described by boundary value problems for system of functional differential equations. For such equations, the theory of boundary value problems, while very important by itself, is also of much interest in relation to the study of asymptotic properties of solutions on unbounded intervals.
The objectives include the investigation of the existence and uniqueness of a solution to boundary value problems for functional differential equations and systems in R^n and more general spaces and the study of their properties.
WWW: http://www.math.cas.cz/homepage/main_page.php?id_membre=19
The research topic and supervisor needs to be approved by the Scientific Board of the Faculty of Science.
The objective is to study asymptotic and oscillation theory of differential equations and differential systems of real orders.
Before initiating the formal application process to doctoral studies, the interested candidates are required to contact the potential advisor for informal discussion.
Many phenomena in nature have oscillatory character and their mathematical models have led to the research of limit periodic, almost periodic, and asymptotically almost periodic sequences. In particular, the attention is paid to special constructions of such sequences in general metric spaces.
Concerning examples, see:
1. M. Veselý; P. Hasil. Asymptotically almost periodic solutions of limit periodic difference systems with coefficients from commutative groups. Topological Methods in Nonlinear Analysis, 2019, 54, no. 2, 515-535. ISSN 1230-3429. doi:10.12775/TMNA.2019.051. 2. M. Veselý; P. Hasil. Values of limit periodic sequences and functions. Mathematica Slovaca, 2016, 66, no. 1, 43-62. ISSN 0139-9918. doi:10.1515/ms-2015-0114. 2. M. Veselý. Construction of almost periodic sequences with given properties. Electronic Journal of Differential Equations, 2008, 2008, no. 126, 1-22. ISSN 1072-6691.
Before initiating the formal application process to doctoral studies, all interested candidates are required to contact Michal Veselý
Partial differential equations (PDE) have important applications in science and engineering. In the realm of linear theory, solutions of PDEs obey the principle of linear superposition, and in some cases, they possess explicit analytical expressions. However, the laws of the nature are not always linear, and nonlinear PDEs play an essential role in modeling these phenomena. The research objective is to bring into light and explain nonlinear phenomena stemming from nonlinear PDEs in connection with singularity theory.
Interested candidates are required to contact directly Phuoc-Tai Nguyen (via email: ptnguyen@math.muni.cz) for informal discussions before initiating the formal application process to doctoral studies.
Before initiating the formal application process to doctoral studies, the interested candidates are required to contact the potential advisor for informal discussion.
Výzkum se zaměří na flexibilní statistické metody a modely, zejména neparametrické a semiparametrické (například aditivní modely, spliny a penalizační metody), v kontextu cenzorovaných, longitudinálních, funkcionálních a jiných dat, s motivacemi pocházejícími zejména z oblasti biomedicínského výzkumu (např. výzkum HIV).
pro Karolínu Hurdálkovou
Objectives: Statistical methodologies dealing with functional data are called Functional Data Analysis (FDA), where the term “functional” emphasizes the
fact that the data are functions characterizing the curves and surfaces.
Aim: The theoretical aspects of FDA will be developed in more detail,
especially connected to practical situations. Our aim is to take up these challenges by giving both theoretical and practical support for more flexible models.
Examples of potential student doctoral projects:
Práce bude zaměřena na modelování růstu a diseminace nádorů pomocí PDEs (reaction-diffusion, pattern formation).
Očekává se spolupráce s Masarykovým onkologickým ústavem a St.Andrews University (GB).
Cílem výzkumného zaměření je studium a vývoj vybraných mnohorozměrných statistických metod v metabolomike, např. analýza hlavních komponent a parciální metoda nejmenších čtverců, a to jak z pohledu numerické-matematického, tak z pohledu mnohorozměrných statistických vizualizací a animací. Vlastnosti těchto metod budou hodnoceny pomocí různých simulačních studií. Metody budou implementovány v jazyce R a aplikovány na reálná data z oblasti medicíny. Toto zameranie vznikolo v spolupráci s Ústavom neuroimunológie SAV, Bratislava.
Výzkum bude zaměřen na teorii extrémních hodnot a její aplikace v oblasti hydrologie a aktuárské matematiky.
Práce se bude zaměřovat na studium prostorových a časoprostorových
metod a modelů, např. kriging, zobecněné aditivní modely, dynamické
časoprostorové modely. Zkoumány budou jejich statistické a numerické vlastnosti
i vizualizační techniky v souvislosti s aplikacemi v oblasti klimatologie,
meteorologie, hydrologie a jiných.
pro Jana Holuba
Cílem práce bude studovat a analyzovat spřažené dynamické systémy, ve kterých dochází k synchronizaci a k jevům, které s ní souvisejí. Základním přístupem k problému budou moderní metody teorie bifurkací a nelineární dynamiky, numerické kontinuační metody a vhodné využití matematické reformulace problému. Aplikace budou směřovány k popisu neuronální sítě (modely neuronů).
Provided by | Faculty of Science | |
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Type of studies | Doctoral | |
Mode | full-time | Yes |
combined | Yes | |
Study options | single-subject studies | No |
single-subject studies with specialization | Yes | |
major/minor studies | No | |
Standard length of studies | 4 years | |
Language of instruction | Czech | |
Doctoral board and doctoral committees |
Consultant
E‑mail: |
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