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See detailOn the eigenvariety of Hilbert modular forms at classical parallel weight one points with dihedral projective image
Deo, Shaunak UL

in Transactions of the American Mathematical Society (2018), 370(6), 3885-3912

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See detailCompatible systems of symplectic Galois representations and the inverse Galois problem I. Images of projective representations
Arias De Reyna Dominguez, Sara UL; Dieulefait, Luis; Wiese, Gabor UL

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 ▲]

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See detailConstant mean curvature foliation of domain of dependence in AdS3
Tamburelli, Andrea UL

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 ▲]

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See detailSpectral synthesis for flat orbits in the dual space of weighted group algebras of nilpotent Lie groups
Ludwig, Jean; Molitor-Braun, Carine UL; Poguntke, Detlev

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

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See detailOn modular forms and the inverse Galois problem
Dieulefait, Luis; Wiese, Gabor UL

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 ▲]

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See detailDifferentiable conjugacy for groups of area preserving circle diffeomorphisms
Monclair, Daniel UL

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 ▲]

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