International Cooperation
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Grant: GF16-34860L
from 01/01/2016
to 31/12/2018
Grantor: Austrian Science Foundation (FWF) - Czech Science Foudation
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Logic and Topology in Banach spaces
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Objectives:
The project is devoted to the study of topological and geometric properties of Banach spaces and their duals, aiming at a better understanding of their structure. Properties of the weak topology often imply important geometric properties of the Banach space in question. On the other hand, geometric properties of the Banach space often give information about its weak topology. Similar statements are true for duals of Banach spaces with the weak-star topology. We are going to explore this interplay in detail. The main project goals are:
1. Developing new tools for constructing and studying Banach spaces, using techniques from set theory and category theory.
2. Exploring different types of networks and related concepts in weak topologies, determining connections with renorming theory.
Results of Goal 1 will lead to new examples, settling some of the problems concerning interplay between geometric and topological properties of non-separable Banach spaces. Goal 2 will lead to a better understanding of the weak topology and its relations to the geometric structure of a Banach space.
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Grant: GF15-34700L
from 01/01/2015
to 31/12/2017
Grantor: Austrian Science Foundation (FWF) - Czech Science Foudation
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The continuum, forcing and large cardinals
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Objectives:
The work shall study interactions between large cardinals and forcing and also with regard to properties of the continuum. The work shall be divided into three subtopics:
(1) First subtopic is called "Combinatorial properties of cardinals and the continuum function". The focus shall be on the impact of several combinatorial properties on the continuum function (a function which maps kappa to the size of the powerset of kappa). As Easton showed, without extra assumptions, there is very little ZFC can prove about the continuum function on regulars. However, once we start to consider large cardinals, or in general combinatorial properties often formulated in the context of large cardinals (tree property, square principles, etc.), suddenly the situation is much more interesting. Subtopic 1 studies these connections.
(2) Second subtopic is called"Combinatorial characteristics of the continuum and the Mathias forcing". This subtopic focuses on the real line from the point of certain combinatorial characteristics which shall be studied by means of the Mathias forcing. This forcing is determined by a filter on the powerset of omega. Thus it is natural to study the connections between the combinatorial properties of filters and the properties of the real line. This subtopic combines set theory and topology.
(3) The third subtopic is called "New developments in the template iterations." Template iterations is a modern forcing method with the potential to show new results regarding the combinatorial characteristics of the real line. Among the main problems to be studied are: obtaining cardinal characteristics with singular values, application of template iterations on non-definable posets, and finally the application of the method with the mixed finite and countable support. These new approaches will be useful in obtaining new results.
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Grant: 7AMB15AT035
from 01/01/2015
to 31/12/2016
Grantor: Ministry of Education, Youth and Sports - MŠMT
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Topics in set theory: Traces of large cardinals, variants of Hechler's theorem, and ultrafilters on countable sets
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Objectives:
The goal of the project is to expand the collaboration between specialists working in different areas of Set Theory. We shall, in particular, try to exploit the complementary expertise of the Czech and Austrian teams while solving problems on the borders of traditional areas of research (large cardinals, forcing, infinitary combinatorics, topology) and encourage mutual cross-fertilization and inspiration sharing. The main goal is to encourage new members of both Czech and Austrian research teams to interact in join international research, to explore new possibilities for scientific collaboration, and to introduce international contacts enabling applications for funding with more ambitious join projects in future years.
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Grant: MUSIC(LH13012)
from 01/03/2013
to 31/12/2015
Grantor: Ministry of Education, Youth and Sports - MŠMT
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Multilevel supervisory control
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Programme type: KONTAKT II
Objectives:
The aim of the project is to develop techniques to decrease computational complexity of supervisory control of discrete-event systems with large number of states. Both automata with known modular structure given by the synchronous product of smaller components and large automata without such a structure will be considered. Standard centralized control methods cannot be applied for complexity reasons, and therefore, we will propose multi-level coordination control with hierarchical structure of the coordinators on different layers for different groups of subsystems. It will be based on the single-level coordination control with one central coordinator that we have recently developed. These efficient techniques will be applied to decentralized control of systems without known modular structure. As a by-product communication protocols between groups of subsystems given by the structure of coordinators on different levels of hierarchy will be obtained.
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Grant: M100191201
from 01/07/2012
to 30/06/2015
Grantor: Academy of Sciences of the Czech Republic
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Algebraic classification of tensors on Lorentzian manifolds and its applications
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Objectives:
We will search for exact vacuum solutions of generalized theories of gravity using the algebraic classification of tensors and the generalization of the Geroch-Held-Penrose formalism to higher dimensions co-developed by our department. Particular focus is on so called universal solutions – vacuum solutions to all theories of gravity derived from the Lagrangian constructed from the metric, the Riemann tensor and its arbitrary covariant derivatives. Another objective is to develop a refinement of the algebraic classifications of tensors in five dimensions.
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Grant: 7AMB12FR003
from 01/01/2012
to 31/12/2013
Grantor: Ministry of Education, Youth and Sports - MŠMT
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Non-linear analysis in Banach spaces
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Programme type: MOBILITY - France
Objectives:
The goal of this project is to contribute to a better understanding of the following topics:
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Archived International Cooperation
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Grant: MEB091101
from 01/01/2011
to 31/12/2012
Grantor: Ministry of Education, Youth and Sports - MŠMT
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Spectral theory of linear operators and reflexivity
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Programme type: MOBILITY - Slovenia
Objectives:
Research in the field of spectral theory of linear operators.
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Grant: MEB021108
from 01/01/2011
to 31/12/2012
Grantor: Ministry of Education, Youth and Sports - MŠMT
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Holomorphic function spaces and their operators
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Programme type: MOBILITY - France
Objectives:
Study of holomorphic functions spaces and related operators (Toeplitz, Hankel, Bergman projection, etc.) and their interplay with the Berezin transform. Where appropriate, extensions to spaces of harmonic functions may also be investigated.
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Grant: MEB0810045
from 01/01/2010
to 31/12/2011
Grantor: Ministry of Education, Youth and Sports - MŠMT
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Unilateral dynamic contact problems for thin structures
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Programme type: MOBILITY - Slovakia
Objectives:
To prove solvability of dynamic contact problems for different models (e.g. Reisne-Mindlin etc.) of plates and shells. Publication of results in the form of scientific papers and then in a monograph about the topic.
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Grant: MEB051006
from 01/01/2010
to 31/12/2011
Grantor: Ministry of Education, Youth and Sports - MŠMT
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Set theory and its applications
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Programme type: MOBILITY - Polsko
Objectives:
Cooperation in the subject of descriptive set theory and forcing. Finishing the book "Ideals and Equivalences", coothored by Jindřich Zapletal and Marcin Sabok. Organizing bilateral conferences in Prague and Hejnice on the subject of infinite games, set theory, and forcing. Lectures of Jindřich Zapletal at the Institute of Mathematics in Wroclaw.
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Grant: MEB021024
from 01/01/2010
to 31/12/2011
Grantor: Ministry of Education, Youth and Sports - MŠMT
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Variational inequalities in equilibrial optimization
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Programme type: MOBILITY - France
Objectives:
Development of tools of variational analysis suitable for study of local properties of solutions of variational inequalities.
Analysis of the stability and sensibility of multi-valued mappings which assign suitable sets of solutions to the data of problems or to perturbing parameters.
Application of obtained results on selected equilibrial problems of continuum mechanics and of mathematical economy.
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Grant: MEB060909
from 01/01/2009
to 31/12/2010
Grantor: Ministry of Education, Youth and Sports - MŠMT
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Set theory and its applications
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Programme type: MOBILITY - Austria
Objectives:
Exploring the interaction between set theory on one hand, and abstract analysis and combinatorics on the the other.
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Grant: MEB090905
from 01/01/2009
to 31/12/2010
Grantor: Ministry of Education, Youth and Sports - MŠMT
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Spectral theory of linear operators and reflexivity
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Programme type: MOBILITY
Objectives:
Study of questions of spectral theory of linear operators concerning the reflexivity.
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