References of "Schlenker, Jean-Marc 50003017"
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See detailHigher signature Delaunay decompositions
Danciger, Jeffrey; Maloni, Sara; Schlenker, Jean-Marc UL

E-print/Working paper (2016)

A Delaunay decomposition is a cell decomposition in R^d for which each cell is inscribed in a Euclidean ball which is empty of all other vertices. This article introduces a generalization of the Delaunay ... [more ▼]

A Delaunay decomposition is a cell decomposition in R^d for which each cell is inscribed in a Euclidean ball which is empty of all other vertices. This article introduces a generalization of the Delaunay decomposition in which the Euclidean balls in the empty ball condition are replaced by other families of regions bounded by certain quadratic hypersurfaces. This generalized notion is adaptable to geometric contexts in which the natural space from which the point set is sampled is not Euclidean, but rather some other flat semi-Riemannian geometry, possibly with degenerate directions. We prove the existence and uniqueness of the decomposition and discuss some of its basic properties. In the case of dimension d = 2, we study the extent to which some of the well-known optimality properties of the Euclidean Delaunay triangulation generalize to the higher signature setting. In particular, we describe a higher signature generalization of a well-known description of Delaunay decompositions in terms of the intersection angles between the circumscribed circles. [less ▲]

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See detailSmall circulant complex Hadamard matrices of Butson type
Hiranandani, Gaurush; Schlenker, Jean-Marc UL

in European Journal of Combinatorics (2016), 51

We study the circulant complex Hadamard matrices of order nn whose entries are llth roots of unity. For n=ln=l prime we prove that the only such matrix, up to equivalence, is the Fourier matrix, while for ... [more ▼]

We study the circulant complex Hadamard matrices of order nn whose entries are llth roots of unity. For n=ln=l prime we prove that the only such matrix, up to equivalence, is the Fourier matrix, while for n=p+q,l=pqn=p+q,l=pq with p,qp,q distinct primes there is no such matrix. We then provide a list of equivalence classes of such matrices, for small values of n,ln,l. [less ▲]

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See detailPolyhedra inscribed in a quadric and anti-de Sitter geometry
Schlenker, Jean-Marc UL

in Oberwolfach Reports (2016)

A short survey on recent results concerning polyhedra inscribed in quadrics.

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See detailVariétés lorentziennes plates vues comme limites de variétés anti-de Sitter, d'après Danciger, Guéritaud et Kassel
Schlenker, Jean-Marc UL

in Astérisque (2016), 380

A survey on the recent work of Danciger, Gu\'eritaud and Kassel on Margulis space-times and complete anti-de Sitter space-times. Margulis space-times are quotients of the 3-dimensional Minkowski space by ... [more ▼]

A survey on the recent work of Danciger, Gu\'eritaud and Kassel on Margulis space-times and complete anti-de Sitter space-times. Margulis space-times are quotients of the 3-dimensional Minkowski space by (non-abelian) free groups acting propertly discontinuously. Goldman, Labourie and Margulis have shown that they are determined by a convex co-compact hyperbolic surface S along with a first-order deformation of the metric which uniformly decreases the lengths of closed geodesics. Danciger, Gu\'eritaud and Kassel show that those space-times are principal ℝ-bundles over S with time-like geodesics as fibers, that they are homeomorphic to the interior of a handlebody, and that they admit a fundamental domain bounded by crooked planes. To obtain those results they show that those Margulis space-times are "infinitesimal" versions of 3-dimensional anti-de Sitter manifolds, and are lead to introduce a new parameterization of the space of deformations of a hyperbolic surface that increase the lengths of all closed geodesics. [less ▲]

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See detailAnti-de Sitter space: from physics to geometry
Schlenker, Jean-Marc UL

in CMS Notes (2015), 47(3), 14-15

A survey of recent developments in anti-de Sitter geometry.

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See detailPolyhedra inscribed in a hyperboloid and anti-de Sitter geometry
Schlenker, Jean-Marc UL

Speeches/Talks (2015)

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See detailThree applications of anti-de Sitter geometry
Schlenker, Jean-Marc UL

Speeches/Talks (2015)

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See detailThe renormalized volume of quasifuchsian manifolds
Schlenker, Jean-Marc UL

Speeches/Talks (2015)

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See detailPolyèdres inscrits dans des quadriques
Schlenker, Jean-Marc UL

Speeches/Talks (2015)

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See detailA cyclic extension of the earthquake flow II
Bonsante, Francesco; Mondello, Gabriele; Schlenker, Jean-Marc UL

in Annales Scientifiques de l'Ecole Normale Supérieure (2015), 48(4), 811859

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See detailProductivity and Mobility in Academic Research: Evidence from Mathematicians
Dubois, Pierre; Rochet, Jean-Charles; Schlenker, Jean-Marc UL

in Scientometrics (2014), 98(3), 1669-1701

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See detailSubmatrices of Hadamard matrices: complementation results
Banica, Teo; Nechita, Ion; Schlenker, Jean-Marc UL

in Electronic Journal of Linear Algebra (2014), 27

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See detailRecovering the geometry of a flat spacetime from a background radiation
Bonsante, F.; Meusburger, C.; Schlenker, Jean-Marc UL

in Annales Henri Poincare (2014), 15(9), 1733-1799

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See detailCollisions of particles in locally AdS spacetimes II. Moduli of globally hyperbolic spaces
Barbot, Thierry; Bonsante, Francesco; Schlenker, Jean-Marc UL

in Communications in Mathematical Physics (2014), 327(3), 691-735

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See detailThe convex core of quasifuchsian manifolds with particles
Lecuire, Cyril; Schlenker, Jean-Marc UL

in Geometry and Topology (2014), 18(4), 2309--2373

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See detailSymplectic Wick rotations between moduli spaces of 3-manifolds
scarinci, carlos; Schlenker, Jean-Marc UL

in Scuola Normale Superiore di Pisa. Annali. Classe di Scienze (2014)

Given a closed hyperbolic surface $S$, let $\cQF$ denote the space of quasifuchsian hyperbolic metrics on $S\times\R$ and $\cGH_{-1}$ the space of maximal globally hyperbolic anti-de Sitter metrics on $S ... [more ▼]

Given a closed hyperbolic surface $S$, let $\cQF$ denote the space of quasifuchsian hyperbolic metrics on $S\times\R$ and $\cGH_{-1}$ the space of maximal globally hyperbolic anti-de Sitter metrics on $S\times\R$. We describe natural maps between (parts of) $\cQF$ and $\cGH_{-1}$, called ``Wick rotations'', defined in terms of special surfaces (e.g. minimal/maximal surfaces, CMC surfaces, pleated surfaces) and prove that these maps are at least $C^1$ smooth and symplectic with respect to the canonical symplectic structures on both $\cQF$ and $\cGH_{-1}$. Similar results involving the spaces of globally hyperbolic de Sitter and Minkowski metrics are also described. These 3-dimensional results are shown to be equivalent to purely 2-dimensional ones. Namely, consider the double harmonic map $\cH:T^*\cT\to\cTT$, sending a conformal structure $c$ and a holomorphic quadratic differential $q$ on $S$ to the pair of hyperbolic metrics $(m_L,m_R)$ such that the harmonic maps isotopic to the identity from $(S,c)$ to $(S,m_L)$ and to $(S,m_R)$ have, respectively, Hopf differentials equal to $i q$ and $-i q$, and the double earthquake map $\cE:\cT\times\cML\to\cTT$, sending a hyperbolic metric $m$ and a measured lamination $l$ on $S$ to the pair $(E_L(m,l), E_R(m,l))$, where $E_L$ and $E_R$ denote the left and right earthquakes. We describe how such 2-dimensional double maps are related to 3-dimensional Wick rotations and prove that they are also $C^1$ smooth and symplectic. [less ▲]

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See detailAnalytic aspects of the circulant Hadamard conjecture
Banica, Teo; Nechita, Ion; Schlenker, Jean-Marc UL

in Annales mathématiques Blaise Pascal (2014), 21

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See detailThe renormalized volume and the volume of the convex core of quasifuchsian manifolds
Schlenker, Jean-Marc UL

in Mathematical Research Letters (2013), 20(4), 773-786

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See detailA cyclic extension of the earthquake flow I
Bonsante, Francesco; Mondello, Gabriele; Schlenker, Jean-Marc UL

in Geometry and Topology (2013), 17(1), 157--234

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See detailVolume maximization and the extended hyperbolic space
Luo, Feng; Schlenker, Jean-Marc UL

in Proceedings of the American Mathematical Society (2012), 140(3), 1053--1068

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