Prof. Bernd Ammann und Mitarbeiter, Zimmer 119

Mohameden Ould Ahmedou, Gießen

Conformal metrics of prescribed Q-curvature on 4-manifolds: A Morse theoretical approach

In this talk we address the question of existence, on a four dimensional riemannian manifold, of conformal metrics of prescribed Q-curvature. The Q-curvature is a generalization on four manifolds of the two dimensional Gauß curvature. This scalar quantity turns out be helpful in the understanding of the topology and geometry of four manifolds. This problem amounts to solve a fourth order nonlinear PDE involving the Paneitz operator. This PDE enjoys a variational formulation, however the corresponding Euler-Lagrange functional does not satisfy the Palais-Smale condition. In this talk we will report on recent existence results obtained through a Morse theoretical approach to this noncompact variational problem combined with a refined analysis of the singularities of the corresponding gradient flow.

Seunghun Hong

The Borel-Weil-Bott theorem via the equivariant McKean-Singer formula

Borel-Weil-Bott theorem states that irreducible representations of a compact connected Lie group G can be constructed by calculating the sheaf cohomologies of holomorphic sections of complex line bundles over the flag variety G/T associated to various T-representations. This result can be understood as an equivariant index theorem for a Dirac operator on G/T. In this talk we shall explain how this index theorem can be easily reached using Kostant's cubic Dirac operator and the equivariant McKean-Singer formula.
Bernd Ammann, 4.11.2014 oder später