Objectif "The proposed project will advance our knowledge in the field of model theory and its applications to functional analysis and Banach space geometry. The research will mobilize recently developed powerful model theoretic techniques in order to throw more light on important and basic questions in Banach space theory. The project will enhance exchange of ideas and techniques between different areas of mathematics, especially stability theory within model theory and Banach space theory.Specifically, we propose to explore connections between model theoretic stability and geometric structure of a fixed Banach space, as well as an elementary class of Banach spaces. The main idea is that stability leads to deeper understanding of spreading models in the ultra-powers of a structure. The project will continue and expand the work of Krivine and Maurey, who proved that stabilityimplies the existence of an almost isometric copy of an l_p space. One of the questions we are going to address is whether weaker versions of stability entail the existence of isomorphic copies of basic sequence spaces.Another question that we will investigate has to do with the phenomenon of categoricity. A class of Banach spaces is called categorical if it has a unique structure (up to isometry) of some uncountable density. We have recently shown that any such class is strongly related to the class of Hilbert spaces, affirming a 35-year old Henson's Conjecture. Recent developments suggest stronger geometric forms of the conjecture, which we will address.In addition, we propose to investigate an analogous conjecture for categoricity under isomorphisms (instead of isometries), which is a much more challenging problem. However, given recent progress in ""geometric stability theory"" in the context of Banach spaces (due to the my collaborators and myself), we are confident that many interesting results are within reach now." Champ scientifique natural sciencesmathematicspure mathematicsalgebralinear algebranatural sciencesmathematicspure mathematicsdiscrete mathematicsmathematical logicnatural sciencesmathematicspure mathematicsmathematical analysisfunctional analysisnatural sciencesmathematicspure mathematicsgeometry Programme(s) FP7-PEOPLE - Specific programme "People" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013) Thème(s) FP7-PEOPLE-2012-CIG - Marie-Curie Action: "Career Integration Grants" Appel à propositions FP7-PEOPLE-2012-CIG Voir d’autres projets de cet appel Régime de financement MC-CIG - Support for training and career development of researcher (CIG) Coordinateur THE HEBREW UNIVERSITY OF JERUSALEM Contribution de l’UE € 47 916,67 Adresse EDMOND J SAFRA CAMPUS GIVAT RAM 91904 Jerusalem Israël Voir sur la carte Type d’activité Higher or Secondary Education Establishments Contact administratif Hani Ben (Ms.) Liens Contacter l’organisation Opens in new window Site web Opens in new window Coût total Aucune donnée Participants (1) Trier par ordre alphabétique Trier par contribution de l’UE Tout développer Tout réduire THE OPEN UNIVERSITY Participation terminée Israël Contribution de l’UE € 52 083,33 Adresse UNIVERSITY ROAD Raanana Voir sur la carte Type d’activité Higher or Secondary Education Establishments Contact administratif Daphna Idelson (Dr.) Liens Contacter l’organisation Opens in new window Site web Opens in new window Coût total Aucune donnée