Graf, Asymptotic completeness for N-body short-range quantum systems: A new proof, Comm. Gromov, H. Lawson, Positive scalar curvature and the Dirac operator on complete Riemannian manifolds, Publicationes Math. IHES 58 , 83— Gromov, M. Shubin, Von Neumann spectra near zero, Geom. Anal, and Funct. Guillemin, D. Kazhdan, Some inverse spectral results for negatively curved 2-manifolds, Topology 19 , — Ikeda, On lens spaces which are isospectral but not isometric, Ann. Kac, Can one hear the shape of a drum?

Koyama, Determinant expression of Selberg zeta functions I, Trans.

Lax, R. Phillips, Scattering theory for automorphic forms, Annals Math.

### Spectral Theory and Geometric Analysis

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Milnor, Whitehead torsion, Bull. Milnor, Eigenvalues of the Laplace operator on certain manifolds, Proc. Annalen , — Pure Appl Math. McKean, I. Singer, Curvature and the eigenvalues of the Laplacian, J. Geometry 1 , 43— Moeglin, J.

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II, — Melrose, Weyl asymptotic for the phase in obstacle scattering Comm. Partial Diff. Equations 13 , — Minakshisundaram, A. Pleijel, Some properties of the eigenfunctions of the Laplace operator on Riemannian manifolds, Canadian J. Moscovici, L 2 index of elliptic operators on locally symmetric spaces of finite volume, Contemp. Moscovici, R. Stanton, R-torsion and zeta functions for locally symmetric manifolds, Invent. Math, Soc. Nachrichten , — Novikov, M.

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## Spectral geometry

Shubin, Morse inequalities and von Neumann invariants of nonSimply connected manifolds, Uspekhi Matem. Nauk 41 , Osgood, R. Phillips, P. Dan Jane The effect of the Ricci flow on magnetic topological entropy Suppose, on a given closed 2-manifold, we have a family of negatively curved metrics that satisfy the Ricci flow.

Anthony Manning showed in that the topological entropy associated to the geodesic flow of a metric is decreasing as we move along the path. We extend this result to a magnetic setting, where the Ricci Yang-Mills flow is a more appropriate geometric evolution equation. I describe some examples and theorems depending on the mean, intrinsic or extrinsic curvature of the surface. Julie Marie Rowlett The Laplace and length spectra of asymptotically hyperbolic manifolds Asymptotically hyperbolic manifolds are a natural generalization of infinite volume hyperbolic manifolds and enjoy similar features.

These results include: a dynamical wave trace formula relating the Laplace and length spectra, a prime orbit theorem for the geodesic flow based on the dynamical zeta function, and a relationship between the pure point spectrum of the Laplacian and the topological entropy of the geodesic flow. Key techniques and ideas from the proofs will be summarized, concluding with a discussion of open problems.

### Submission history

Andrea Sambusetti On the growth of quotients of Klenian groups. Notice that, as these quotient groups naturally act on non-simply connected quotients of a Cartan-Hadamard manifold, the classical arguments of Patterson-Sullivan's theory topology of the boundary, shadows, quasi-conformal densities etc.

- Workshop on Spectral Geometry and Analysis of Differential Operators?
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- The Hardy inequality.
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- On the geometry of diffusion operators and stochastic flows;
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This forces us to a more elementary approach for counting points in the orbit of a quotient which gives a new elementary proof of the classical results of divergence of geometrically finite groups in the simply connected case. We also notice that, contrary to the simply connected case, there is large freedom for the behaviour of the growth function of quotients of Kleinian groups even convex-cocompact : as a way of example, we will exhibit quotients of convex cocompact Kleinian groups with mixed polynomial-exponential growth.

Dal'Bo, M. Peigne, J. Primary MSC: 30 ; 35 ; Applied Math? MAA Book? Electronic Media?

## Spectral Theory and Geometry : E. Brian Davies :

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