Termine

For an asymptotically locally Euclidean (ALE) or asymptotically locally flat (ALF) gravitational instanton (M,g) with toric symmetry, we express the signature of (M,g) directly in terms of its rod structure. Applying Hitchin?Thorpe-type inequalities for Ricci-flat ALE/ALF manifolds, we formulate necessary conditions that the rod structures of toric ALE/ALF instantons must satisfy, as a step toward a classification of such spaces. Finally, we apply these results to the study of rod structures with three turning points.

Further information

Further information

Further information

We discuss the (1+1)-dimensional wave maps equation with values in a compact Riemannian manifold M. Motivated by the Gibbs measure problem, we consider Brownian paths on the manifold M as initial data. Our main theorem is the probabilistic local well-posedness of the associated initial value problem. The analysis in this setting involves analytic, geometric, and probabilistic aspects. This is joint work with J. Lührmann and G. Staffilani. 1

We study deterministic and stochastic homogenisation problems for free discontinuity functionals under new hypotheses on the surface energies. The results are based on a compactness theorem with respect to Gamma-convergence, on the characterisation of the integrands of the Gamma-limit by means of limits of minimum values of some auxiliary minimum problems on small cubes, and on the subadditive ergodic theorem for the stochastic part.

We give a non-asymptotic estimate for the spectral norm of a large class of random matrices that is sharp in many cases. We also obtain strong asymptotic freeness for certain sparse Gaussian matrices. Joint work with Afonso Bandeira and Ramon van Handel.