Chance and Chandra

A few examples are given of Chandra’s work on statistical and stochastic problems that relate to open questions in astrophysics, in particular his theory of dynamical relaxation in systems with inverse-square interparticle forces. The roles of chaos and integrability in this theory require clarification, especially for systems having a dominant central mass. After this prelude, a hypothetical form of bosonic dark matter with a simple but nontrivial statistical mechanics is discussed. This makes for a number of eminently falsifiable predictions, including some exotic consequences for dynamical friction.     

A RATIO OF INTEGRATION BETWEEN QUOTIENTS IN GEOMETRIC INVARIANT THEORY

Let T be a maximal torus of a connected reductive group G that acts linearly on a projective variety X so that all semi-stable points are stable. This paper compares the integration on the geometric invariant theory quotient X//G of Chow classes σ to the integration on the geometric invariant theory quotient X//T of certain lifts of σ twisted by c _top(g/t), the top Chern class of the T-equivariant vector bundle induced by the quotient of the adjoint representation on the Lie algebra of G by that of T. We provide a purely algebraic proof that the ratio between any two such integrals is an invariant of the group G and that it equals the order of the Weyl group whenever the root system of G decomposes into irreducible root systems of type A _n , for various $ n\in \mathbb{N} $ . As a corollary, we are able to remove this restriction on root systems by applying a related result of Martin from symplectic geometry.