Date du début: 1 août 2016,
Date de fin: 31 juil. 2021,
The Atiyah-Singer index theorem was one of the most spectacular achievements of mathematics in the XXth century, connecting the analytic and topological properties of manifolds. The Baum-Connes conjecture is a hugely successful approach to generalizing the index theorem to a much broader setting. It has remarkable applications in topology and analysis. For instance, it implies the Novikov conjectu ...
Date du début: 1 janv. 2016,
Date de fin: 31 déc. 2019,
The Project aims to make significant advances to the field of noncommutative geometry by developing new methods through substantial interaction within sub-fields of noncommutative geometry and two other areas of pure mathematics. The main focus will be to determine the topological non-triviality of new types of quantum fibrations. Also, we aim to construct quantum metric geometries of crossed prod ...
Date du début: 1 mars 2013,
Date de fin: 28 févr. 2018,
"The direct principal aim of the project is twofold. First, to attract best qualified young researchers from all over the world and offer them top expertise in diverse fields of mathematical research so as to significantly develop their scientific potential and thus stimulate their successful careers. Second,to strengthen the international dimension of IMPAN's recruitment policy, to wide open it ...
Date du début: 1 sept. 2013,
Date de fin: 31 août 2017,
The aim of the project is to investigate the phenomenon of universality in Topological Dynamics. Universality is a classical and fundamental subject in Dimension Theory. The introduction of universality to the context of dynamics is more recent but has already proven itself to be fruitful. The far reaching Lindenstrauss -Tsukamoto Conjecture is the claim that mean dimension and periodic dimension ...
Date du début: 1 janv. 2013,
Date de fin: 31 déc. 2016,
"The ``FLUX'' project is devoted to the mathematical analysis of an array of problems originating from different domains of real world applications. They include: fluid mechanics, aerodynamics, geophysics, phase transitions and image processing, meteorology. The language for rigorous formulation of models of these phenomena is the theory of partial differential equations. In addition, we face free ...
Date du début: 1 janv. 2013,
Date de fin: 31 déc. 2016,
"This is a project for a partnership between leading Brazilian and European research groups in dynamical systems, a prominent subject in mathematics. An extensive consortium of European and Brazilian institutions will collaborate to provide world leading critical mass and support for research on the very forefront of the field. Work Packages reflect parallel priorities in the research. Transfer o ...
Date du début: 1 nov. 2012,
Date de fin: 31 oct. 2016,
"The theory of asymptotic behaviour of operator semigroups is a comparatively new field serving as a common denominator for many other areasof mathematics, such as for instance the theory of partial differential equations, complex analysis, harmonic analysis and topology.The primary interest in the study of asymptotic properties of strongly continuous operator semi-groups comes from the fact that ...
Date du début: 1 juin 2014,
Date de fin: 31 mai 2016,
The Institute of Mathematics of the Polish Academy of Sciences is a leading research institution in Poland in the area of pure and applied mathematics. A part of its mission is to provide high education for mathematicians, and to prepare them to work both in research and financial institutions, as well as in industry. Erasmus+ programme is supposed to contribute to some extent to implement this mi ...
Date du début: 1 mai 2011,
Date de fin: 30 avr. 2014,
"The aim of this project is the study of complicated, chaotic dynamics. In the project we will investigate local aspects of dynamics, like dynamics of pairs, n-tuples, or dynamics over sets. Particular, we will be interested in pairs chaotic in the sense of Li and Yorke, entropy pairs, independent sets, etc. We will search for connections between shadowing property and chaos, especially these that ...
Date du début: 1 janv. 2009,
Date de fin: 31 déc. 2012,
"In precise mathematical terms, the goal of the project is to develop and apply K-theory and spectral geometry for Galois-type extensions of noncommutative algebras. We seek verifiable criteria to distinguish different isomorphism classes of principal extensions of noncommutative algebras and K-theory -classes of modules associated to them. On the geometric side, we aim to achieve a new guiding pr ...
Date du début: 1 oct. 2010,
Date de fin: 30 sept. 2012,
"The project lies at the intersection of functional analysis, probability theory and quantum algebra, with possible applications to mathematical physics. It is broadly concerned with the analysis of evolutions of systems related to quantum groups, using the language of noncommutative probability. The latter, which extends the classical stochastic theory, is necessary to describe random phenomena e ...
Date du début: 1 avr. 2008,
Date de fin: 1 août 2011,
"The first part of the project is concerned with a classification of the orbit equivalence relation E coming from the conjugation action of the group of all diffeomorphisms of class C2 on itself. A well-known example given by Arnold shows that there exist C2 diffeomorphisms of the circle with equal rotation numbers, which are not conjugate by any smooth mapping. This raises a natural question as t ...
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