The Kahler-Ricci flow provides a useful method of deforming any Kahler metric towards a caononical metric. In this talk, we will discuss on recent progress on the Kahler-Ricci flow and how the flow behaves on manifolds with positive Kodaira dimension and without Kahler-Einstein metrics.

Inspired by an old idea of von Neumann, we seek a pair of commuting operators X,P which are, in a specific sense, 'close' to the canonical non-commuting position and momentum operators, x,p. Difficulties with von Neumann's original idea (involving an alleged orthogonalization of the coherent states) are discussed. Here these difficulties are avoided by restricting attention to operators acting on density matrices which are reasonably decohered (i.e., spread out in phase space). Such operators could be of use in discussions of emergent classicality from quantum mechanics. Moreover, they may be used to give a discussion of the relationship between exact and approximate decoherence in the decoherent histories approach to quantum theory.

In this talk I will describe the phenomenology associated with neutrino oscillations and I will review the evidence for neutrino mass from solar and atmospheric neutrino experiments, as well as from the most important laboratory searches for neutrino oscillations. I will also briefly discuss the main implications for theory.

The decade 1963-1973 is sometimes referred to as the 'golden age' of black hole research. Mathematical theorems proved in this period led to a complete classical description of equilibrium black holes in four space-time dimensions. More recently, string theory has forced us to take seriously the possibility of extra spatial dimensions. Thinking about black holes in more than four dimensions has led to spectacular advances in our understanding of quantum gravity. In the last five years, we have learned that higher-dimensional black holes exhibit much richer behaviour than four-dimensional ones, even classically. I shall review the discoveries of this new 'silver age' of black hole research. The talk should be accessible to MSc students.

Within supersymmetric grand unified theories, cosmic strings are generically formed at the end of a hybrid inflationary era. However, cosmic microwave background measurements imply severe constraints on the allowed cosmic strings contribution to the temperature anisotropies. In the framework of supersymmetry, I will study F- and D-term inflation and I will set constraints on the free parameters (mass scales and couplings) of the models, so that there is compatibility between mixed models (inflation + cosmic strings) and current measurements. Recently there is a revival in interest for cosmic strings, since ina ddition, superstrings could play the role of cosmic strings in theories with large extra dimensions and moreover it may be that cosmic strings have been already seen in the sky.

Within supersymmetric grand unified theories, cosmic strings are generically formed at the end of a hybrid inflationary era. However, cosmic microwave background measurements imply severe constraints on the allowed cosmic strings contribution to the temperature anisotropies. In the framework of supersymmetry, I will study F- and D-term inflation and I will set constraints on the free parameters (mass scales and couplings) of the models, so that there is compatibility between mixed models (inflation + cosmic strings) and current measurements. Recently there is a revival in interest for cosmic strings, since ina ddition, superstrings could play the role of cosmic strings in theories with large extra dimensions and moreover it may be that cosmic strings have been already seen in the sky.