1.2. GeometryProgramme leaders: S.J. Edixhoven, G.B.M. van der Geer
This programme focuses on geometry and its relations with and implications in mathematical physics. The program covers both algebraic as well as analytic, real and symplectic geometry and the developments arising from the interplay with physics. This interaction has an enormous potential for both geometry and physics. Central topics in the study of geometry are moduli spaces (in particular of curves, abelian varieties and vector bundles), contact structures; in mathematical physics the central topics are field theories, string theory and mirror symmetry. Also applications of algebraic geometry (esp. curves) in coding theory are studied.
Status of the programme.
Current topics cover the full range of aspects of geometry: algebraic, analytic, real and symplectic. Central topics are moduli spaces of curves, abelian varieties and K3 surfaces, also in positive characteristics; the topic of contact structures is new. In mathematical physics the developments center around M-theory and string duality, with emphasis on the application to enumerative geometry, moduli spaces of vector bundles, and automorphic forms.