5. November 2020



(University of Miami – USA)

Title: Initial data rigidity results
Abstract: We present several rigidity results for initial data sets motivated by the positive mass theorem. An important step in our proofs is to establish conditions that ensure that a marginally outer trapped surface is “weakly outermost”. A rigidity result for Riemannian manifolds with a lower bound on their scalar curvature is included as a special case. Relevant background on marginally outer trapped surfaces will be discussed. This talk is based on joint work with Michael Eichmair and Abraão Mendes.



1. October 2020



(KTH Stockholm – Sweden)

Title: On highly anisotropic big bang singularities. 
Abstract: In cosmology, the universe is typically modelled by spatially homogeneous and isotropic solutions to Einstein’s equations. However, for large classes of matter models, such solutions are unstable in the direction of the singularity. For this reason, it is of interest to study the anisotropic setting. 
The purpose of the talk is to describe a framework for studying highly anisotropic singularities. In particular, for analysing the asymptotics of solutions to linear systems of wave equations on the corresponding backgrounds and deducing information concerning the geometry.
The talk will begin with an overview of existing results. This will serve as a background and motivation for the problem considered, but also as a justification for the assumptions defining the framework we develop. 
Following this overview, the talk will conclude with a rough description of the results.