We prove a dynamical wave trace formula for asymptotically hyperbolic (n+1) dimensional manifolds with negative (but not necessarily constant) sectional curvatures which equates the renormalized wave trace to the lengths of closed geodesics. This result generalizes the classical theorem of Duistermaat-Guillemin for compact manifolds and the results of GuillopéZworski, Perry, and Guillarmou-Naud...

– Consider uniformly elliptic random walk on Z with independent jump rates across nearest neighbour bonds of the lattice. We show that the infinite volume effective diffusion matrix can be almost surely recovered as the limit of finite volume periodized effective diffusion matrices.  2003 Éditions scientifiques et médicales Elsevier SAS MSC: 60K37; 60K35; 74Q20

Given a noncompact quasi-Fuchsian surface in a finite volume hyperbolic 3–manifold, we introduce a new invariant called the cusp thickness, that measures how far the surface is from being totally geodesic. We relate this new invariant to the width of a surface, which allows us to extend and generalize results known for totally geodesic surfaces. We also show that checkerboard surfaces provide e...

In this paper we prove the convergence of a nite volume scheme to the solution of a Stefan problem, namely the nonlinear diiusion equation ut ?'(u) = v, together with a homogeneous Neumann boundary condition and an initial condition. This is done by means of a priori estimates in L 1 and use of Kolmogorov's theorem on relative compactness of subsets of L 2 .

We study the convergence of the Finite Volume Scheme for the advection equation with a divergence free C1 speed in a domain without boundary. We show that the rate of the L∞(0, T ;L1)-error estimate is h1/2 for BV data. This result was expected from numerical experiment and is optimal. The proof is based on Kuznetsov’s method. This method has been introduced for non-linear hyperbolic equations ...

We code the wave-front tracking algorithm for Hughes’ model of pedestrian motion with generalized running cost. This model displays a non-classical dynamic at the splitting point between the two directions of motion. The wave-front tracking scheme provides us with reference solutions to test numerically the convergence of classical finite volume schemes, which do not treat explicitly the dynami...

In this paper we are interested in computing representations of the fundamental group of a 3-manifold into PSL(3,C) (in particular in PSL(2,C),PSL(3,R) and PU(2, 1)). The representations are obtained by gluing decorated tetrahedra of flags as in [11, 1]. We list complete computations (giving 0-dimensional or 1-dimensional solution sets) for the first complete hyperbolic non-compact manifolds wi...

The theory of Coxeter groups is used to provide an algebraic construction of finite volume hyperbolic manifolds. Combinatorial properties of finite images of these groups can be used to compute the volumes of the resulting manifolds. Three examples, in 4, 5 and 6-dimensions, are given, each of very small volume, and in one case of smallest possible volume.