1.2. Geometry
Programme 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.
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