GRK 870: Arithmetic and Geometry

点击翻译按钮获取中文摘要

The aim of this International Research Training Group with ETH and University of Zurich is basic research on recent problems in the areas of Arithmetic Geometry and Number Theory, Differential Geometry and Geometric Analysis as well as Complex Geometry. The following topics are included.Arithmetic Geometry and Number Theory:-- cohomological construction of arithmetic Chow rings-- arithmetic Riemann-Roch theorem for automorphic vector bundles-- explicit formulae for arithmetic Chern numbers of automorphic vector bundles-- bounds for Arakelov invariants-- computations of rings of Picard modular forms-- arithmetic intersection theory on Picard modular surfaces-- representations of p-adic groups and Number Theory-- Langlands functoriality for central simple algebrasDifferential Geometry and Geometric Analysis:-- foundation of a symplectic field theory-- holomorphic curves, Hamiltonian dynamics and symplectic topology-- spectral characterisation of isolated singularities-- spectral properties and estimates for eigenvalues of Dirac operators-- special geometries and spinor field equations in string theory-- special geometric structures in Lorentzian geometry-- holonomy groups for indefinite metrics in the non-irreducible caseComplex Geometry:-- geometry of moduli spaces for vector bundles and applications-- geometry of special complex varieties-- Krichever correspondence-- Cauchy-Riemann equation on complex manifolds-- Grauert-Oka principle and deformation theory of holomorphic vector bundlesThe Research Training Group¿s training contains a study programme, in which the scholarship holders can on the one hand, increase their knowledge in the named areas to enlarge it to a wider basis and on the other hand, they can deepen their knowledge for their own doctoral thesis. First results of their recent research projects are being exchanged with the other scholarship holders in the framework of the college seminar.The PhD students from Berlin and Zurich receive important impulses for their work within the scope of a common yearly summer school and half-yearly mini courses for which renowned speakers are invited. The graduate programme furthermore includes an exchange programme for the scholarship holders between Berlin and Zurich.