Objectif This proposal is concerned with the homological properties of Calabi-Yau threefolds, the geometric structures which play a crucial role in string theory. Rather than working directly with categories of sheaves, we focus on a closely-related class of models defined using quivers with potentials, which have themselves been the subject of intensive research over the last decade.Associated to a quiver with potential are two complex manifolds: the space of stability conditions and the cluster variety. Recent work by physicists Gaiotto, Moore and Neitzke suggests that there is a remarkable geometric relationship between these spaces, involving Donaldson-Thomas invariants and the Kontsevich-Soibelman wall-crossing formula. Work by the PI and others over the last couple of years has paved the way for a rigorous mathematical understanding of this relationship. This has the potential to open up new vistas in algebra and geometry, as well as greatly enhancing our understanding of the mathematics of quantum field theory.Our proposal combines powerful general constructions with specific computable examples. We will work initially with a class of examples related to triangulated surfaces; here the relevant spaces can be identified with familiar objects in the topology of surfaces, including moduli spaces of quadratic differentials, projective structures and local systems. These examples already involve deep mathematics, and are closely related to quantum field theories of current interest in theoretical physics.This proposal involves an unusually wide range of mathematics. Our ambition is to assemble a team of 4 research assistants having a sufficiently broad expertise to make progress on this exciting multi-disciplinary project. The PI is in a perfect position to lead such a team: he invented stability conditions, carried out important work on Donaldson-Thomas invariants, and proved a major theorem which forms one of the starting points of the proposal. Champ scientifique natural sciencesmathematicspure mathematicstopologynatural sciencesphysical sciencesquantum physicsquantum field theorynatural sciencesmathematicspure mathematicsalgebranatural sciencesphysical sciencestheoretical physicsstring theorynatural sciencesmathematicspure mathematicsgeometry Programme(s) H2020-EU.1.1. - EXCELLENT SCIENCE - European Research Council (ERC) Main Programme Thème(s) ERC-ADG-2014 - ERC Advanced Grant Appel à propositions ERC-2014-ADG Voir d’autres projets de cet appel Régime de financement ERC-ADG - Advanced Grant Institution d’accueil THE UNIVERSITY OF SHEFFIELD Contribution nette de l'UE € 1 556 550,00 Adresse FIRTH COURT WESTERN BANK S10 2TN Sheffield Royaume-Uni Voir sur la carte Région Yorkshire and the Humber South Yorkshire Sheffield 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 € 1 556 550,00 Bénéficiaires (1) Trier par ordre alphabétique Trier par contribution nette de l'UE Tout développer Tout réduire THE UNIVERSITY OF SHEFFIELD Royaume-Uni Contribution nette de l'UE € 1 556 550,00 Adresse FIRTH COURT WESTERN BANK S10 2TN Sheffield Voir sur la carte Région Yorkshire and the Humber South Yorkshire Sheffield 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 € 1 556 550,00
