Objective
This proposal comprises two Euro Summer Schools on topics of Topology. The first event (Proper Actions) will take place the week before a PhD EuroConference on Homotopy Theory which will be held in he same location. Thus, the purpose of the first event is to provide training by specialists on a very active current field of research, addressed to young researchers who will profit from both the Summer School and the PhD EuroConference. The subject of the first event is the Baum-Connes Conjecture, relating the equivariant K -theory of the classifying space for proper actions of a discrete group G with the algebraic K-theory of the reduced group C*-algebra of G. The index map constructed by Baum and Connes between these two mathematical objects generalises the Atiyah index map for G-equivariant elliptic pseudo-differential operators on a principal G-manifold. This subject has deep multidisciplinary features, as it combines algebraic, analytic, and topological aspects of group actions, and it has implications in various domains of mathematics.
The second event (Geometric 3-Manifolds) has been scheduled close to the 2002 Barcelona Conference on Algebraic Topology, also with the aim of promoting the participation of young researchers in consecutive events. The subject of this event is Thurston's geometrisation programme of 3-manifolds, which is nowadays in the Core of 3-dimensional topology. This programme has contributed to enlarge the spectrum of mathematics used in 3-dimensional topology. Besides using tools from other fields, mainly from geometry, it has contributed to develop other subjects, for instance in complex analysis, with McMullen's work on Poincaré series for Riemann surfaces and iteration on the Teichmüller space.
ftp://ftp.cordis.lu/pub/improving/docs/HPCF-2000-00140-2.pdf(opens in new window)
Fields of science (EuroSciVoc)
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
- natural sciences mathematics pure mathematics algebra
- natural sciences mathematics pure mathematics topology algebraic topology
- natural sciences mathematics pure mathematics geometry
- natural sciences mathematics pure mathematics mathematical analysis complex analysis
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Coordinator
Spain
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