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
2011

Combinatorial differential geometry and ideal Bianchi–Ricci identities
Advances in Geometry, year: 2011, volume: 11, edition: 3, DOI

Comparison theorems for Riccati inequalities arising in the theory of PDE's with pLaplacian
Electron. J. Differential Equations, year: 2011, volume: 2011, edition: 53

Conformal cloak for waves
Physical Review A, year: 2011, volume: 83, edition: 5, DOI

Considerable Sets of Linear Operators in Hilbert Spaces as Operator Generalized Effect Algebras
Foundations of Physics, year: 2011, volume: 41, edition: 10, DOI

Controlling birefringence in dielectrics
Nature Photonics, year: 2011, volume: 5, edition: 6, DOI

Covariant Lagrange multiplier constrained higher derivative gravity with scalar projectors
Physics Letters B, year: 2011, volume: 701, edition: 1, DOI

Critical higher order SturmLiouville difference operators
J. Difference Equ. Appl., year: 2011, volume: 17, edition: 9

Critical oscillation constant for halflinear differential equations with periodic coefficients
Annal. Mat. Pura Appl., year: 2011, volume: 190, edition: 3

Describing periodicity in twoway deterministic finite automata using transformation semigroups
Developments in Language Theory: 15th International Conference, DLT 2011, Milan, Italy, July 1922, 2011. Proceedings, year: 2011

Eigenvalue and oscillation theorems for time scale symplectic systems
International Journal of Dynamical Systems and Differential Equations, year: 2011, volume: 3, edition: 12