Brazil-France interplays in Gauge Theory, extremal structures and stability – BRIDGES
Following Berger's holonomy classification and Atiyah and Donaldson's achievements in Yang-Mills theory, differential geometers have studied the interactions between variational and algebraic perspectives. Our project combines these traditions in the study of special geometric structures, such as extremal Kähler/Sasaki, special holonomy, generalized geometry and the interplay of all these concepts in Ströminger systems. In practice, these problems belong to gauge theory : a space of connections, a curvature equation to solve, a group of symmetries to control. In each case, the expected outcome is a correspondence between a special geometry and an algebraic condition, as provided by Kobayashi-Hitchin-D-U-Y, which allows to describe the local structure of the moduli space in terms of stability. In addition to constructing new families of examples, our objective is to understand their global topology, deformations and algebraic obstructions.
Project coordination
Eveline Legendre (Institut Camille Jordan)
The author of this summary is the project coordinator, who is responsible for the content of this summary. The ANR declines any responsibility as for its contents.
Partner
IMT Institut de Mathématiques de Toulouse
ICJ Institut Camille Jordan
LMO Laboratoire de mathématiques d'Orsay
LMJL - U. Nantes LABORATOIRE DE MATHEMATIQUES JEAN LERAY
LMAP Laboratoire de mathématiques et de leurs applications - Pau
Universidade Federal do Rio de Janeiro / Instituto de Matematica
Universite de Campinas / IMECC
IMB INSTITUT DE MATHEMATIQUES DE BOURGOGNE - UMR 5584
LMBA LABORATOIRE DE MATHEMATIQUES DE BRETAGNE ATLANTIQUE
UFF Universidade Federal Fluminense / Instituto de Matematica
Help of the ANR 391,641 euros
Beginning and duration of the scientific project:
March 2022
- 48 Months
