# Pieter Blue: On the stability of higher dimensions

**Time: **
Tue 2019-11-26 11.00 - 12.00

**Location: **
Seminar Hall Kuskvillan, Institut Mittag-Leffler

**Participating: **
Pieter Blue, University of Edinburgh

### Abstract

There is a large class of Kaluza-Klein type spaces given by the Cartesian product of \(1+n\) dimensional Minkowski space with a Ricci-flat Riemannian manifold, called the internal space. These are solutions of the Einstein equation. This talk will show that these spaces are stable as solutions of the Einstein equation when n is sufficiently large and, at least, when the internal space is a torus.

This requires taking the intersection of methods for quasilinear wave and Klein-Gordon equations. This stability result is a related to a conjecture of Penrose concerning the validity of string theory.