Closed geodesics and flat tori in spectral theory on symmetric spaces

David Gurarie

Displaying similar documents to “Closed geodesics and flat tori in spectral theory on symmetric spaces”

Spectral invariants for coupled spin-oscillators

San Vũ Ngọc (2011-2012)

Séminaire Laurent Schwartz — EDP et applications

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This text deals with in a semiclassical setting. Given a quantum system, the haunting question is “What interesting quantities can be discovered on the spectrum that can help to characterize the system ?” The general framework will be semiclassical analysis, and the issue is to recover the classical dynamics from the quantum spectrum. The coupling of a spin and an oscillator is a fundamental example in physics where some nontrivial explicit calculations can be done.

Two lectures on spectral invariants for the Schrödinger operator

Mikhail V. Novitskii (1999-2000)

Séminaire de théorie spectrale et géométrie

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A splitting formula for the spectral flow of the odd signature operator on 3-manifolds coupled to a path of $S U (2)$ connections.

Himpel, Benjamin (2005)

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Spectral resonances for the Laplace-Beltrami operator

Stephen De Bièvre, Peter D. Hislop (1988)

Annales de l'I.H.P. Physique théorique

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The distribution of eigenvalues of partial differential operators

D. G. Vassiliev (1991-1992)

Séminaire Équations aux dérivées partielles (Polytechnique)

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Normal form of the wave group and inverse spectral theory

Steve Zelditch (1998)

Journées équations aux dérivées partielles

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This talk will describe some results on the inverse spectral problem on a compact riemannian manifold (possibly with boundary) which are based on V. Guillemin's strategy of normal forms. It consists of three steps : first, put the wave group into a normal form around each closed geodesic. Second, determine the normal form from the spectrum of the laplacian. Third, determine the metric from the normal form. We will try to explain all three steps and to illustrate with simple examples...

Tetra and Didi, the cosmic spectral twins.

Doyle, Peter G., Rossetti, Juan Pablo (2004)

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Maximally degenerate laplacians

Steven Zelditch (1996)

Annales de l'institut Fourier

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The Laplacian $Δ_{g}$ of a compact Riemannian manifold $(M, g)$ is called if its eigenvalue multiplicity function $m_{g} (k)$ is of maximal growth among metrics of the same dimension and volume. Canonical spheres $(S^{n}, can)$ and CROSSes are MD, and one asks if they are the only examples. We show that a MD metric must be at least a Zoll metric with just one distinct eigenvalue in each cluster, and hence with all band invariants equal to zero. The principal band invariant is then calculated in terms of geodesic integrals...