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Constant Gauss curvature foliations of AdS spacetimes with particles Schlenker, Jean-Marc ; in Transactions of the American Mathematical Society (in press) 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 ▲] Detailed reference viewed: 44 (6 UL)On the eigenvariety of Hilbert modular forms at classical parallel weight one points with dihedral projective image Deo, Shaunak in Transactions of the American Mathematical Society (2018), 370(6), 3885-3912 Detailed reference viewed: 324 (19 UL)Compatible systems of symplectic Galois representations and the inverse Galois problem I. Images of projective representations Arias De Reyna Dominguez, Sara ; ; Wiese, Gabor 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 ▲] Detailed reference viewed: 186 (23 UL)Constant mean curvature foliation of domain of dependence in AdS3 Tamburelli, Andrea in Transactions of the American Mathematical Society (2016) We prove that, given an acausal curve in the boundary at infinity of Anti-de Sitter space which is the graph of a quasi-symmetric homeomorphism, there exists a foliation of its domain of dependence by ... [more ▼] We prove that, given an acausal curve in the boundary at infinity of Anti-de Sitter space which is the graph of a quasi-symmetric homeomorphism, there exists a foliation of its domain of dependence by constant mean curvature surfaces with bounded second fundamental form. Moreover, these surfaces provide a family of quasi-conformal extensions of the quasi-symmetric homeomorphism we started with. [less ▲] Detailed reference viewed: 101 (13 UL)Spectral synthesis for flat orbits in the dual space of weighted group algebras of nilpotent Lie groups ; Molitor-Braun, Carine ; in Transactions of the American Mathematical Society (2013), 365(8), 4433-4473 Detailed reference viewed: 96 (6 UL)On modular forms and the inverse Galois problem ; Wiese, Gabor in Transactions of the American Mathematical Society (2011), 363(9), 4569--4584 In this article new cases of the Inverse Galois Problem are established. The main result is that for a fixed integer n, there is a positive density set of primes p such that PSL_2(F_{p^n}) occurs as the ... [more ▼] In this article new cases of the Inverse Galois Problem are established. The main result is that for a fixed integer n, there is a positive density set of primes p such that PSL_2(F_{p^n}) occurs as the Galois group of some finite extension of the rational numbers. These groups are obtained as projective images of residual modular Galois representations. Moreover, families of modular forms are constructed such that the images of all their residual Galois representations are as large as a priori possible. Both results essentially use Khare's and Wintenberger's notion of good-dihedral primes. Particular care is taken in order to exclude nontrivial inner twists. [less ▲] Detailed reference viewed: 98 (2 UL)Differentiable conjugacy for groups of area preserving circle diffeomorphisms Monclair, Daniel 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 ▲] Detailed reference viewed: 80 (1 UL) |
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