Central Compact Objects in Supernova Remnants

Central Compact Objects (CCOs) are a handful of sources located close to the geometrical center of young supernova remnants. They only show thermal-like, soft X-ray emission and have no counterparts at any other wavelength. While the first observed CCO turned out to be a very peculiar magnetar, discovery that three members of the family are weakly magnetised Isolated Neutron Stars (INSs) set the basis for an interpretation of the class. However, the phenomeology of CCOs and their relationship with other classes of INSs, possibly ruled by supernova fall-back accretion, are still far from being well understood.Comment: 7 pages, to appear in the proceedings of "Physics of Neutron Stars - 2017" Conference (July 10-14, Saint Petersburg), JPCS, eds. G.G. Pavlov, J.A. Pons, P.S. Shternin & D.G. Yakovle

Non-Equilibrium Steady State generated by a moving defect: the supersonic threshold

We consider the dynamics of a system of free fermions on a 1D lattice in the presence of a defect moving at constant velocity. The defect has the form of a localized time-dependent variation of the chemical potential and induces at long times a Non-Equilibrium Steady State (NESS), which spreads around the defect. We present a general formulation which allows recasting the time-dependent protocol in a scattering problem on a static potential. We obtain a complete characterization of the NESS. In particular, we show a strong dependence on the defect velocity and the existence of a sharp threshold when such velocity exceeds the speed of sound. Beyond this value, the NESS is not produced and remarkably the defect travels without significantly perturbing the system. We present an exact solution for a $\delta-$like defect traveling with an arbitrary velocity and we develop a semiclassical approximation which provides accurate results for smooth defects.Comment: 18 pages, 13 figure

The Decomposition Theorem and the topology of algebraic maps

We give a motivated introduction to the theory of perverse sheaves, culminating in the Decomposition Theorem of Beilinson, Bernstein, Deligne and Gabber. A goal of this survey is to show how the theory develops naturally from classical constructions used in the study of topological properties of algebraic varieties. While most proofs are omitted, we discuss several approaches to the Decomposition Theorem, indicate some important applications and examples.Comment: 117 pages. New title. Major structure changes. Final version of a survey to appear in the Bulletin of the AM

What is a perverse sheaf?

Three-page article on the notion of perverse sheaf to appear in the "What is?" series in the Notices of the AMS.Comment: to appear in the May 2010 issue of the Notices of the AMS http://www.ams.org/notice

The perverse filtration and the Lefschetz Hyperplane Theorem

We describe the perverse filtration in cohomology using the Lefschetz Hyperplane Theorem.Comment: Revised version with minor changes. To appear in Annals of Mathematic