MODPRINBUN · MODULI OF PRINCIPAL G-BUNDLES OVER CURVES

The applicant Christian Pauly plans to stay at the emerging geometry group of the ICMAT (Insituto de Ciencias Matematicas) at the CSIC (Consejo Superior de Investigaciones Cientificas) in Madrid. The proposal describes three research tasks related to principal G-bundles over projective varieties, which have seen recent important progress (strange duality of generalised theta functions, construction of moduli spaces in any characteristic). Special attention is given to the case when the base variety is a curve. Links with conformal field theory and string theory enrich this subject (Verlinde formula) and lead to interesting new problems. The research is carried out in collaboration with several members of the research group: Luis Alvarez-Consul, Tomas Gomez and Oscar Garcia-Prada. Training for the applicant will be provided by the research group in gauge theory and symplectic geometry.