Mira Fernandes Lectures on Mathematical Relativity 

20/06/2013, 14:00 — 15:00 — Room P3.10, Mathematics Building
Hans Ringström, KTH, Stockholm

On the stability and topology of the universe (IV)

In these lectures, a brief general introduction to the Cauchy problem in general relativity will be given. Moreover, some examples of hyperbolic formulations of the equations will be discussed. The proof of the existence of a maximal globally hyperbolic development will also be sketched, including a discussion of the analysis background. Turning to global issues, choices of equations that are appropriate in order to prove global existence in the case of a positive cosmological constant will be presented. Finally, a proof of global existence will be sketched in that setting.

See also

Hans_R_Lisbon_2013.pdf

19/06/2013, 14:00 — 15:00 — Room P3.10, Mathematics Building
Hans Ringström, KTH, Stockholm

On the stability and topology of the universe (III)

In these lectures, a brief general introduction to the Cauchy problem in general relativity will be given. Moreover, some examples of hyperbolic formulations of the equations will be discussed. The proof of the existence of a maximal globally hyperbolic development will also be sketched, including a discussion of the analysis background. Turning to global issues, choices of equations that are appropriate in order to prove global existence in the case of a positive cosmological constant will be presented. Finally, a proof of global existence will be sketched in that setting.

18/06/2013, 14:00 — 15:00 — Room P3.10, Mathematics Building
Hans Ringström, KTH, Stockholm

On the stability and topology of the universe (II)

In these lectures, a brief general introduction to the Cauchy problem in general relativity will be given. Moreover, some examples of hyperbolic formulations of the equations will be discussed. The proof of the existence of a maximal globally hyperbolic development will also be sketched, including a discussion of the analysis background. Turning to global issues, choices of equations that are appropriate in order to prove global existence in the case of a positive cosmological constant will be presented. Finally, a proof of global existence will be sketched in that setting.

17/06/2013, 15:00 — 16:00 — Room P3.10, Mathematics Building
Hans Ringström, KTH, Stockholm

On the stability and topology of the universe (I)

The current standard model of the universe is spatially homogeneous, isotropic and spatially flat. Furthermore, the matter content is described by two perfect fluids (dust and radiation) and there is a positive cosmological constant. Such a model can be well approximated by a solution to the Einstein-Vlasov equations with a positive cosmological constant. As a consequence, it is of interest to study stability properties of solutions in the Vlasov setting. The talk will contain a description of recent results on this topic. Moreover, the restriction on the global topology of the universe imposed by the data collected by observers will be discussed.

See also

Hans Ringström's slides