A note on spacelike and timelike compactness

When studying the causal propagation of a field in a globally hyperbolic spacetime M, one often wants to express the physical intuition that it has compact support in spacelike directions, or that its support is a spacelike compact set. We compare a number of logically distinct formulations of this idea, and of the complementary idea of timelike compactness, and we clarify their interrelations. E.g., a closed subset A of M has a compact intersection with all Cauchy surfaces if and only if A is contained in J(K) for some compact set K. (However, it does not suffice to consider only those Cauchy surfaces that partake in a given foliation of M.) Similarly, a closed subset A of M is contained in a region between two Cauchy surfaces if and only if the intersection of A with J(K) is compact for all compact K. We also treat future and past compact sets in a similar way

Effects of flavor conserving CP violating phases in SUSY models

I summarize our recent works on the effects of flavor conserving CP violating phases in SUSY models on $B$ and $K$ phenomenology.Comment: Contributed alk at the 3rd International Conference on B Physics and CP Violation (BCONF99), Taipei, Taiwan, 3-7 Dec 1999 (4 pages

The topology and geometry of contact structures in dimension three

The goal of this article is to survey recent developments in the theory of contact structures in dimension three.Comment: 13 pages. To appear in the ICM 2006 proceeding