First Minho Meeting on
Mathematical Physics

Lode Wylleman (Gent University, Belgium)
Classification results on purely electric or magnetic perfect fluids

Perfect fluids for which the Weyl tensor is purely electric or purely magnetic wrt the flow lines are either of Petrov type D or I. I will review the complete invariant classification of the type D case, thereby introducing the ortho-complex-null formalism and briefly mentioning some related results. Then conjectures and theorems regarding Petrov type I non-accelerating models - so called (anti-)Newtonian universes - will be surveyed.

Josep Llosa (University of Barcelona, Spain)
Flat deformation of a pseudo-Riemannian metric

A pseudo-Riemannian metric in a n-manifold has n(n+1)/2 independent components but, as n of them can be chosen arbitrarily by an appropriate choice of coordinates, the metric has n(n-1)/2 degrees of freedom. As many as the number of components of a differential 2-form. We shall prove (for any number of dimensions) that any analytic pseudo-Riemannian metric g can be deformed into a flat metric h (or a constant curvature metric) by a deformation law like: h_mn := a g_mn - F²_mn, where F²_mn:=F_mp g^pq F_qn and a is a scalar function fulfilling an arbitrary prescribed scalar relation. We shall further explore the possible implications of this result in general relativity.

Maria Conceição Carvalho (FCUL, University of Lisbon, Portugal)

Entropy production for the Boltzmann equation via an N-particle collision model

In 1956, Mark Kac proposed a novel approach to the study of the Boltzmann equation via the large N limit of a system of N particles undergoing binary collisions. In the 1960's, Henry McKean and his students made many significant contributions to this program, particularly with regard to the problem of propagation of chaos. However, analysis of the rate of equilibriation for this model remained an open problem for many years, and progress on this front was much more recent. Until now, this progress has been made for what corresponds to "Maxwellian molecules". Recent work of myself, Carlen and Loss extends this progress to the physically significant hard-sphere case. This talk will be aimed at a general mathematical audience and we shall assume nothing in the way of familiarity with Kac's program, or even the Boltzmann equation.

Marc Mars (University of Salamanca, Spain)
A selection of recent progress and open problems in Mathematical Relativity

I will discuss some recent results in the physics of classical black holes in the context of mathematical relativity. I will focus on three aspects: uniqueness theorems of stationary vacuum black holes in four-dimensions, the Penrose inequality and marginally outer trapped surfaces and their evolution.

José Edelstein (University of Santiago de Compostela, Spain)
The AdS/CFT correspondence: selected topics

We introduce the AdS/CFT correspondence or Maldacena conjecture with special emphasis on some selected topics including strongly coupled phenomena in non-Abelian gauge theory and the holographic description of relativistic (conformal) hydrodynamics.

Raul Vera (University of the Basque Country, Bilbao, Spain)
Signature-changing submanifolds: hypersurface layer construction by gluing

This talk is a review of a formalism for a unified description of the traditional construction of timelike (or spacelike) thin layers, such as shells, branes and domain walls, together with the signature-changing, or pure null, ones. One particular aim is to analyze the possibility of having branes whose causal character changes from point to point in order to provide a regular and consistent description of signature change, and study some of its properties.