Termine

*Abstract*: Rational ellipticity is a very strong condition on a topological space, which in particular forces it to have "simple topology''. Given its conjectured relation to manifolds with non-negative sectional curvature, a number of previous works has focused on finding geometric criteria that imply rational ellipticity. In this talk, I will describe a new criterion for a Riemannian G-manifold to be rationally elliptic, which generalizes most of the previously known ones. As an application, we will prove that non-negatively curved manifolds with an infinitesimally polar cohomogeneity 3 action must be rationally elliptic. This is joint work with Elahe Khalili Samani.

wissenschaftliches Kolloquium

To tackle parametric partial differential equations with highly heterogeneous coefficients, we propose an adaptive localized basis construction procedure based on both offline training and online enrichment. First, in the offline phase, a set of problem-adapted local basis functions is precomputed. Next, in the online phase, we use a localized residual-based a posteriori error estimator to investigate the accuracy of the reduced solution for any given new parameter. As the error estimator is localized, we can exploit it to adaptively enrich the reduced solution space locally where needed. The approach thus guarantees the accuracy of reduced solutions given any possibly insufficient reduced basis that was constructed during the offline phase. Numerical experiments demonstrate the efficiency of the proposed method.

The 2d (massless) Sinh-Gordon model is amongst the simplest 2d quantum field theories that are expected to be integrable (= infinitely many symmetries), but without conformal symmetry. In this talk I will explain a rigorous construction of this model and its vertex correlations (= Laplace transforms) on the infinite cylinder using probability theory. In particular, I will explain how the theory of Gaussian multiplicative chaos can be used to analyze the spectrum of the corresponding Sinh-Gordon Hamiltonian. This talk will be based on joint work with Colin Guillarmou and Vincent Vargas.