Objectif Quantum affine algebras are important examples of Drinfeld-Jimbo quantum groups. They can be defined as quantizationsof affine Kac-Moody algebras or as affinizations of finite type quantum groups (Drinfeld Theorem).The representation theory of quantum affine algebras is very rich. It has been studied intensively during the past twenty fiveyears from different point of views, in particular in connections with various fields in mathematics and in physics, such asgeometry (geometric representation theory, geometric Langlands program), topology (invariants in small dimension),combinatorics (crystals, positivity problems) and theoretical physics (Bethe Ansatz, integrable systems).In particular, the category C of finite-dimensional representations of a quantum affine algebra is one of the most studiedobject in quantum groups theory. However, many important and fundamental questions are still unsolved in this field. The aim of the research project is to make significant advances in the understanding of the category C as well as of its applications in the following five directions. They seem to us to be the most promising directions for this field in the next years :1. Asymptotical representations and applications to quantum integrable systems,2. G-bundles on elliptic curves and quantum groups at roots of 1,3. Categorications (of cluster algebras and of quantum groups),4. Langlands duality for quantum groups,5. Proof of (geometric) character formulas and applications.The resources would be used for the following :(1) Hiring of 2 PhD students (in 2015 and 2017).(2) Hiring of 2 Postdocs (in 2015 and 2017).(3) Invitations and travel for ongoing and future scientific collaborations.(4) Organization of a summer school in Paris on quantum affine algebras. Champ scientifique natural sciencesmathematicspure mathematicstopologynatural sciencesmathematicspure mathematicsalgebranatural sciencesmathematicspure mathematicsgeometrynatural sciencesmathematicspure mathematicsdiscrete mathematicscombinatoricsnatural sciencesphysical sciencestheoretical physics Programme(s) H2020-EU.1.1. - EXCELLENT SCIENCE - European Research Council (ERC) Main Programme Thème(s) ERC-CoG-2014 - ERC Consolidator Grant Appel à propositions ERC-2014-CoG Voir d’autres projets de cet appel Régime de financement ERC-COG - Consolidator Grant Institution d’accueil CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS Contribution nette de l'UE € 792 750,00 Adresse RUE MICHEL ANGE 3 75794 Paris France Voir sur la carte Région Ile-de-France Ile-de-France Paris Type d’activité Research Organisations 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 € 1 182 000,00 Bénéficiaires (2) Trier par ordre alphabétique Trier par contribution nette de l'UE Tout développer Tout réduire CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS France Contribution nette de l'UE € 792 750,00 Adresse RUE MICHEL ANGE 3 75794 Paris Voir sur la carte Région Ile-de-France Ile-de-France Paris Type d’activité Research Organisations 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 € 1 182 000,00 Tiers Entité juridique autre qu’un sous-traitant qui est affiliée ou juridiquement liée à un participant. L’entité réalise des travaux dans les conditions prévues par la convention de subvention, fournit des biens ou des services pour l’action, mais n’a pas signé la convention de subvention. Le tiers respecte les règles applicables au participant qui lui est lié dans le cadre de la convention de subvention en ce qui concerne l’éligibilité des coûts et le contrôle des dépenses. UNIVERSITE PARIS CITE France Contribution nette de l'UE € 389 250,00 Adresse 85 BD SAINT GERMAIN 75006 Paris Voir sur la carte Région Ile-de-France Ile-de-France Paris Type d’activité Higher or Secondary Education Establishments Liens Contacter l’organisation 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 € 389 250,00
