Mathematical structures and their physical applications
 Project Identification
 MSM0021622409
 Project Period
 1/2005  12/2011
 Investor / Pogramme / Project type

Ministry of Education, Youth and Sports of the CR
 Research Intents
 MU Faculty or unit

Faculty of Science
 prof. RNDr. Jiří Rosický, DrSc.
 prof. RNDr. Miroslav Bartušek, DrSc.
 doc. RNDr. Martin Čadek, CSc.
 prof. RNDr. Zuzana Došlá, DSc.
 doc. Franz Hinterleitner, Ph.D.
 prof. RNDr. Josef Janyška, DSc.
 doc. RNDr. Jiří Kaďourek, CSc.
 doc. Mgr. Ondřej Klíma, Ph.D.
 doc. Mgr. Josef Klusoň, Ph.D., DSc.
 prof. RNDr. Ivan Kolář, DrSc.
 Mgr. Michael Krbek, Ph.D.
 Mgr. David Kruml, Ph.D.
 prof. RNDr. Radan Kučera, DSc.
 doc. Mgr. Michal Kunc, Ph.D.
 prof. Alexander Lomtatidze, DrSc.
 prof. RNDr. Jana Musilová, CSc.
 prof. RNDr. Jan Paseka, CSc.
 doc. RNDr. Libor Polák, CSc.
 doc. RNDr. Bedřich Půža, CSc.
 prof. RNDr. Jan Slovák, DrSc.
 prof. RNDr. Roman Šimon Hilscher, DSc.
 prof. Rikard von Unge, Ph.D.
 Keywords
 differencial geometry, parabolic geometry, algebraic topology, homotopy theory, quantum gravity, string theory, category theory, algebraic number theory, semigroup and automata theory, differencial equations, difference equations
The subject of the research activity implemented within the research plan is the study of structures of algebra, geometry and analysis and their applications, mainly in physics. This is a very topical and very broad subject belonging to a basic research in mathematics and in mathematical physics, and the research plan concentrates on some of its areas and directions. The most important of them are differential geometry, algebraic topology, quantum gravity, category theory, algebraic number theory, the theory of semigroups and automata, and differential and difference equations. These areas are deeply interrelated. For instance, algebra, analysis, geometry and topology provide mathematical tools for quantum gravity and they have decisively influenced the recent progress in algebraic number theory. On the other hand, they use the language of category theory. Also, mathematical physics in general and quantum gravity in particular provide intuitive understanding of some complicated structures of algebra, geometry and analysis and their mutual relations.
The general research plan objective is to support basic research in mathematics and mathematical physics at the Masaryk University. These are fields in which the Czech Republic in general and the Masaryk University in particular are keeping a highlevel international standard. The aim is to provide necessary conditions for a highly competitive research in these fields at the Masaryk University, which also establish a fruitful background for PhD students and stimulate PhD projects in mainstream topics. The concrete research plan objective is to get new and significant results in all areas of the subject of the research plan contributing to those areas on an international level. These results are communicated at international conferences and published in leading international journals. Some parts of the research are intended to be completed, written down in a monographic form and published by a reputable publishing house.
Publications
Total number of publications: 446
2012

Oscillation and conjugacy criteria for twodimensional symplectic difference systems
Computers and Mathematics with Applications, year: 2012, volume: 64, edition: 7, DOI

Oscillation and spectral theory for linear Hamiltonian systems with nonlinear dependence on the spectral parameter
Mathematische Nachrichten, year: 2012, volume: 285, edition: 1112, DOI

Plane Gravitational Waves and Loop Quantization
Journal of Physics: Conference Series, year: 2012, volume: 360, edition: May, DOI

Rayleigh principle for linear Hamiltonian systems without controllability
ESAIM: Control, Optimisation and Calculus of Variations, year: 2012, volume: 18, edition: 2, DOI

Special phase functions and phase infinitesimal symmetries in classical general relativity
AIP Conf. Proc. 1460,, XX INTERNATIONAL FALL WORKSHOP ON GEOMETRY AND PHYSICS, year: 2012

Towards loop quantization of plane gravitational waves
Classical and Quantum Gravity, year: 2012, volume: 29, edition: 6, DOI

Triple Representation Theorem for homogeneous effect algebras
2012 42ND IEEE INTERNATIONAL SYMPOSIUM ON MULTIPLEVALUED LOGIC (ISMVL), year: 2012
2011

A boundary value problem on a halfline for differential equations with indefinite weight
Commun. Appl. Anal., year: 2011, volume: 15, edition: 24

Absolute instruments and perfect imaging in geometrical optics
New Journal of Physics, year: 2011, volume: 13, edition: 115004, DOI

An asymptotic formula for solutions of nonoscillatory halflinear differential equations
Arch. Math., year: 2011, volume: 47, edition: 1