Description du projet DEENESFRITPL Des formes différentielles sur des espaces analytiques non archimédiens Au début des années 2000, les mathématiciens Kontsevich et Soibelman ont introduit deux variantes de la conjecture SYZ provenant de la théorie des cordes: la première non-archimédienne et la seconde différentielle-géométrique. Les deux conjectures postulent l’existence d’une variété affine singulière. Les deux approches devraient donner le même résultat, avec des variétés affines singulières correspondantes naturellement isomorphes; malheureusement, l’existence d’un tel isomorphisme est désormais remise en question. Financé par le programme Actions Marie Skłodowska-Curie, le projet nalimdif travaille sur de nouveaux outils qui devraient nous permettre d’étudier cette dernière hypothèse et de mieux comprendre les limites de l’effondrement de Gromov-Hausdorff. L’étude proposée repose sur la théorie des formes différentielles sur les espaces analytiques non archimédiens développée par Chambert-Loir et Ducros. Afficher les objectifs du projet Masquer les objectifs du projet Objectif In the beginning of 2000s Kontsevich and Soibelman have introduced two variants of the SYZ conjecture originating from string theory: a non-Archimeadean one and a differential-geometric one. Both of these conjectures posit existence of a singular affine manifold (the base of the SYZ fibration) that can be obtained either as a subset of the non-Archimedean analytic space associated to a family of complex projective Calabi-Yau varieties with maximally unipotent monodromy, or as a Gromov-Hausdorff limit of fibres of the family with Ricci-flat metric in the polarization class and normalized diameter (the latter was also independently conjectured by Gross, Wilson, and Todorov). Recent years have seen active developments in both of these conjectures through work of de Fernex, Kollár, Mustaţa, Nicaise, Xu, Gross, Tosatti, Zhang and others. Kontsevich and Soibelman have also conjectured that both approaches give the same result, with corresponding singular affine manifolds naturally isomorphic; unfortunately, the existence of such an isomorphism is open as of now.The aim of this project is to build tools that will allow both to attack the comparison conjecture and to make progress in the understanding of the collapsing Gromov-Hausdorff limits in the odd-dimensional case (hypekähler case having been extensively studied). The proposed approach is based on the theory of differential forms on non-Archimedean analytic spaces due to Chambert-Loir and Ducros. Firstly, a notion of a non-Archimedean limit of a degenerating family of real forms with values in Chambert-Loir-Ducros forms will be defined. Secondly, the metric structure of the collapsing limit will be described in terms of such non-Archimedean limits of Kähler forms. Thirdly, the canonical affine structure on the limit space conjectured to exist in the metric picture will be studied using non-Archimedean methods, assuming a natural statement about the limits of the solutions of Monge-Ampere equations. Champ scientifique natural sciencesphysical sciencestheoretical physicsstring theory Programme(s) H2020-EU.1.3. - EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions Main Programme H2020-EU.1.3.2. - Nurturing excellence by means of cross-border and cross-sector mobility Thème(s) MSCA-IF-2018 - Individual Fellowships Appel à propositions H2020-MSCA-IF-2018 Voir d’autres projets de cet appel Régime de financement MSCA-IF-EF-ST - Standard EF Coordinateur KATHOLIEKE UNIVERSITEIT LEUVEN Contribution nette de l'UE € 166 320,00 Adresse OUDE MARKT 13 3000 Leuven Belgique Voir sur la carte Région Vlaams Gewest Prov. Vlaams-Brabant Arr. Leuven Type d’activité Higher or Secondary Education Establishments Liens Contacter l’organisation Opens in new window Site web Opens in new window Participation aux programmes de R&I de l'UE Opens in new window Réseau de collaboration HORIZON Opens in new window Coût total € 166 320,00
