Constant Gauss curvature foliations of AdS spacetimes with particles

in Transactions of the American Mathematical Society (2020), 373(6), 4013--4049

We prove that for any convex globally hyperbolic maximal (GHM) anti-de Sitter (AdS) 3-dimensional space-time N with particles (cone singularities of angles less than π along time-like curves), the ... [more ▼]

We prove that for any convex globally hyperbolic maximal (GHM) anti-de Sitter (AdS) 3-dimensional space-time N with particles (cone singularities of angles less than π along time-like curves), the complement of the convex core in N admits a unique foliation by constant Gauss curvature surfaces. This extends, and provides a new proof of, a result of \cite{BBZ2}. We also describe a parametrization of the space of convex GHM AdS metrics on a given manifold, with particles of given angles, by the product of two copies of the Teichm\"uller space of hyperbolic metrics with cone singularities of fixed angles. Finally, we use the results on K-surfaces to extend to hyperbolic surfaces with cone singularities of angles less than π a number of results concerning landslides, which are smoother analogs of earthquakes sharing some of their key properties. [less ▲]

Compatible systems of symplectic Galois representations and the inverse Galois problem I. Images of projective representations

in Transactions of the American Mathematical Society (2017), 369

This article is the first part of a series of three articles about compatible systems of symplectic Galois representations and applications to the inverse Galois problem. In this first part, we determine ... [more ▼]

This article is the first part of a series of three articles about compatible systems of symplectic Galois representations and applications to the inverse Galois problem. In this first part, we determine the smallest field over which the projectivisation of a given symplectic group representation satisfying some natural conditions can be defined. The answer only depends on inner twists. We apply this to the residual representations of a compatible system of symplectic Galois representations satisfying some mild hypothesis and obtain precise information on their projective images for almost all members of the system, under the assumption of huge residual images, by which we mean that a symplectic group of full dimension over the prime field is contained up to conjugation. Finally, we obtain an application to the inverse Galois problem. [less ▲]

Spectral synthesis for flat orbits in the dual space of weighted group algebras of nilpotent Lie groups

in Transactions of the American Mathematical Society (2013), 365(8), 4433-4473

Differentiable conjugacy for groups of area preserving circle diffeomorphisms

in Transactions of the American Mathematical Society (n.d.)

We study groups of circle diffeomorphisms whose action on the cylinder C=S1×S1∖Δ preserves a volume form. We first show that such a group is topologically conjugate to a subgroup of PSL(2,R), then discuss ... [more ▼]

We study groups of circle diffeomorphisms whose action on the cylinder C=S1×S1∖Δ preserves a volume form. We first show that such a group is topologically conjugate to a subgroup of PSL(2,R), then discuss the existence of a differentiable conjugacy. [less ▲]