Ringvorlesung
- Tim Shilkin
- Marc Casals
- James Davies
- Sandra Albrechtsen
Abstract
Part I: "The problem of global unique solvability of the Navier-Stokes equations"
by Timofei Shilkin
May 08, 15, 22, 29
Part II: "Coarse Graph Theory" (TBC)
by Sandra Albrechtsen and James Davies
Date: June 5, 10, 12, 17
When viewed from far away, many graphs and metric spaces appear to have a much simpler "coarse" structure which captures their large-scale geometry. This idea is formalised by the notion of quasi-isometries. For example, string graphs and complete Riemannian planes are both quasi-isometric to planar graphs. The blossoming area of coarse graph theory aims to analyse the coarse structure of graphs and metric spaces.
We give an introduction to coarse graph theory and discuss some recent results. Topics will include coarse Menger's theorem, asymptotic minors, string graphs, asymptotic dimension, and connections to Cayley graphs and Riemannian surfaces.
Part III:
Quasinormal modes of black holes in General Relativity
by Marc Casals
Date: June 19, 26, July 3, 10
Field perturbations of a black hole spacetime can be modelled, during a phase of their evolution known as ringdown, by quasinormal modes: exponentially-damped oscillations whose frequencies and decay rates depend only on the parameters of the black hole. In the specific case of gravitational field perturbations, the Laser Interferometer Gravitational-Wave Observatory has detected waveforms emitted by black hole binary inspirals which were consistent with the theoretical quasinormal mode prediction during the ringdown. In this Ringvorlesung, we will first give a brief introduction to the theory of General Relativity and black holes. We will then study linear field perturbations of black hole spacetimes. After separation of variables, the field equations reduce to ordinary differential equations of Heun type and their analysis will enable us to model the quasinormal mode ringdown.
Recorded lecture
-
The problem of global unique solvability of the Navier-Stokes equations IV
Timofei Shilkin -
Coarse Graph Theory I
Sandra Albrechtsen, James Davies -
Coarse Graph Theory II
Sandra Albrechtsen, James Davies -
Coarse Graph Theory III
Sandra Albrechtsen, James Davies -
Coarse Graph Theory IV
Sandra Albrechtsen, James Davies
