Oberseminare und sonstige Vorträge

5 sessions on professional competences. You can pick and choose: either one, several, or all sessions.
Open to all! All sessions are open to all MM researchers of Mathematics Münster, regardless of their experience level, as all input and exercises are designed for individual needs.
Register via: mm.careers@uni-muenster.de

Modelled on the Anti-de Sitter space, asymptotically Anti-de Sitter spaces can be defined as Lorentzian manifolds that possess a timelike conformal boundary. Due to their lack of global hyperbolicity, finding asymptotically Anti-de Sitter solutions to the Einstein equations (necessarily with a negative cosmological constant) through the Cauchy problem requires tackling the latter as an initial boundary value problem. In this talk, I will present the two known types of geometric boundary conditions leading to the local existence and uniqueness of solutions in dimension 4: the Dirichlet boundary conditions, which were introduced by Friedrich in 1995, and the homogeneous Robin boundary conditions, which I introduced in a recent work.

tba If you are interested please contact Prof. Dr. Anna Siffert (asiffert@uni-muenster.de)

In this talk, I will recall the notions of C*- and W*-superrigidity for groups. I will then present examples of non-amenable groups that can be completely reconstructed from their reduced C*-algebras, but not from their group von Neumann algebras. These groups are constructed as infinite direct sums of amalgamated free product groups and provide the first known examples of non-amenable groups exhibiting this behavior. This is joint work with Juan Felipe Ariza Mejía and Ionut Chifan.

In this talk we survey several results on biconservative submanifolds, with particular emphasis on biconservative hypersurfaces in Euclidean spaces that are invariant under the action of SO(p+1)×SO(q+1). Using the Poincaré?Bendixson Theorem, we analyze the dynamics of their profile curves in the orbit space and establish the existence of infinitely many complete SO(p+1)×SO(q+1)-invariant biconservative hypersurfaces in Euclidean spaces.

Conformal-biharmonic maps arise as critical points of the conformal-bienergy functional, a second-order functional obtained by modifying the classical bienergy functional through curvature terms motivated by conformal geometry. In dimension four, this functional enjoys conformal invariance, making it particularly relevant in the study of variational problems in conformal geometry. In this talk we focus on stability properties of conformal-biharmonic maps. We investigate the conformal-biharmonic stability of the identity map of compact Einstein manifolds with non-negative scalar curvature and show that its conformal-biharmonic index coincides with the classical harmonic index, with a remarkable exception in the case of the four-dimensional sphere. We also study conformal-biharmonic hypersurfaces in space forms and compute the index and nullity for hyperspheres in spheres. Our results reveal new stability phenomena and emphasize the geometric differences between biharmonic and conformal-biharmonic variational theories.

tba If you are interested please contact Prof. Dr. Anna Siffert (asiffert@uni-muenster.de)