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Documents  58J50 | enregistrements trouvés : 64

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Correspondence between Ruelle resonances and quantum resonances for non-compact Riemann surfaces Guillarmou, Colin | CIRM H

Post-edited

Research talks;Partial Differential Equations;Geometry

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Understanding the growth of Laplace eigenfunctions (part 1 of 2) Canzani, Yaiza | CIRM H

Post-edited

Research talks

In this talk we will discuss a new geodesic beam approach to understanding eigenfunction concentration. We characterize the features that cause an eigenfunction to saturate the standard supremum bounds in terms of the distribution of $L^{2}$ mass along geodesic tubes emanating from a point. We also show that the phenomena behind extreme supremum norm growth is identical to that underlying extreme growth of eigenfunctions when averaged along submanifolds. Using the description of concentration, we obtain quantitative improvements on the known bounds in a wide variety of settings. In this talk we will discuss a new geodesic beam approach to understanding eigenfunction concentration. We characterize the features that cause an eigenfunction to saturate the standard supremum bounds in terms of the distribution of $L^{2}$ mass along geodesic tubes emanating from a point. We also show that the phenomena behind extreme supremum norm growth is identical to that underlying extreme growth of eigenfunctions when averaged along ...

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Inverse problems and spectral theory :proceedings of the workshop on spectral theory of differential operators and inverse problems held at Research Institute for Mathematical Science Kyoto University#Oct. 28 - Nov. 1 Isozaki, Hiroshi | American Mathematical Society 2004

Congrès

- 243 p.
ISBN 978-0-8218-3421-3

Contemporary mathematics , 0348

Localisation : Collection 1er étage

opérateur différentiel # théorie spectrale # problème inverse # électromagnétisme # élasticité # équation de Schrödinger # géométrie différentielle # analyse numérique

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Actes de séminaire de théorie spectrale et géométrie. Vol. 25 :année 2006-2007 | Institut Fourier 2008

Congrès

- x, 226 p.

Localisation : Séminaire 1er étage

théorie ergodique # géométrie # dynamique symbolique # combinatoire de mots # billard # transport de mesures # courbure de Ricci # flot quasi-conforme # variété Hadamard # isométrie # opérateur Lamé

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Spectral analysis in geometry and number theory:international conference on the occasion of Toshikazu Sunada's 60th birthdayNagoya # august 6-10, 2007 Kotani, Motoko ; Naito, Hisashi ; Tate, Tatsuya | American Mathematical Society 2009

Congrès

- xii; 342 p.
ISBN 978-0-8218-4269-0

Contemporary mathematics , 0484

Localisation : Collection 1er étage

géométrie spectrale # théorie des nombres # formule des traces # problème isospectrale # fonction zéta # ergodicité quantique # onde aléatoire # analyse géométrique discrète

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Actes du séminaire de théorie spectrale et géométrie. Vol. 26année 2007-2008 | Institut Fourier 2009

Congrès

- 176 p.

Localisation : Séminaire 1er étage

théorie spectrale # EDP # géométrie différentielle

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Spectral theory and geometric analysis.International conference in honor of Mikhail Shubin's 65th birthdayBoston # july 29 - august 2, 2009 Braverman, Maxim ; Friedlander, Leonid ; Kappeler, Thomas ; Kuchment, Peter ; Topalov, Peter ; Weitsman, Jonathan | American Mathematical Society 2011

Congrès

- vii; 213 p.
ISBN 978-0-8218-4948-4

Contemporary mathematics , 0535

Localisation : Collection 1er étage

analyse globale # EDP # problème spectral # opérateur intégral de Fourier # dérivées sur les surfaces de Riemann # équation de Ginzburg-Landau # trou noir

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Pseudo-differential operators: analysis, applications and computations.Selected papers based on lectures presented at the meeting of the ISAAC group in pseudo-differential operators (IGPDO)London # july 13-18, 2009 Rodino, Luigi ; Wong, Man W. ; Zhu, Hongmei | Birkhäuser 2011

Congrès

- vi; 305 p.
ISBN 978-3-0348-0048-8

Operator theory: advances and applications , 0213

Localisation : Collection 1er étage

EDP # opérateurs pseudo-différentiels

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Spectral geometry.Based on the international conferenceDartmouth # july 19-23, 2010 Barnett, Alex H. ; Gordon, Carolyn S. ; Perry, Peter A. ; Uribe, Alejandro | American Mathematical Society 2012

Congrès

- ix; 339 p.
ISBN 978-0-8218-5319-1

Proceedings of symposia in pure mathematics , 0084

Localisation : Collection 1er étage

analyse globale # géométrie spectrale # isospectralité

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Analytic aspects of problems in Riemannian geometry: elliptic PDEs, solitons and computer imagingLandéda # may 9-13, 2005 Baird, Paul ; El Soufi, A. ; Fardoun, A. ; Regbaoui, R. | Société Mathématique de France 2011

Congrès

- xviii; 173 p.
ISBN 978-2-85629-330-0

Séminaires et congrès , 0022

Localisation : Collection 1er étage

Arbre de Steiner # calcul à la machine # champ de vecteurs conformes # compensation # concentration de la courbure # courbure scalaire # EDP non-linéaire elliptique # flot par la courbure # flot par la courbure moyenne # géométrie conforme # intégrabilité # inégalité Hardy-Sobolev # laplacien # meilleure constante # problème de valeur propre # réseau planaire # soliton # solution auto-similaire # surface fermée # surface à courbure moyenne constante # tenseur de Schouten # variété kählerienne # éclatement Arbre de Steiner # calcul à la machine # champ de vecteurs conformes # compensation # concentration de la courbure # courbure scalaire # EDP non-linéaire elliptique # flot par la courbure # flot par la courbure moyenne # géométrie conforme # intégrabilité # inégalité Hardy-Sobolev # laplacien # meilleure constante # problème de valeur propre # réseau planaire # soliton # solution auto-similaire # surface fermée # surface à courbure moyenne ...

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Pseudo-differential operators, generalized functions and asymptotics.Selected papers of the 8th ISAAC congressMoscow # august 22-27, 2011 Molahajloo, Shahla ; Pilipovic, Stevan ; Toft, Joachim ; Wong, M. W. | Birkhäuser 2013

Congrès

- viii; 369 p.
ISBN 978-3-0348-0584-1

Operator theory: advances and applications , 0231

Localisation : Collection 1er étage

opérateur pseudo-différentiel # équation différentielle # équation aux dérivées partielles # groupe topologique

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Fractal geometry and dynamical systems in pure and applied mathematics II: fractals in applied mathematics.PISRS 2011 international conference on analysis, fractal geometry, dynamical systems and economicsMessina # november 2011AMS special session on fractal geometry in pure and applied mathematics: in memory of Benoît MandelbrotBoston # january 2012AMS special session on geometry and analysis on fractal spacesHonululu # march 2012 Carfi, David ; Lapidus, Michel L. ; Pearse, Erin P. J. ; Van Frankenhuijsen, Machiel | American Mathematical Society 2013

Congrès

- viii; 372 p.
ISBN 978-0-8218-9148-3

Contemporary mathematics , 0601

Localisation : Collection 1er étage

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Geometric and spectral analysis.CRM workshop on:geometry of eigenvalues and eigenfucntions, manifolds of metrics and probabilistic methods in geometry and analysis, spectral invariants on non-compact and singular spacesMontréal # June 4-8, July 2-6 and July 23-27, 2012 Albin, Pierre ; Jakobson, Dmitry ; Rochon, Frédéric | American Mathematical Society;Centre De Recherches Mathematiques 2014

Congrès

- x; 366 p.
ISBN 978-1-4704-1043-8

Contemporary mathematics , 0630

Localisation : Collection 1er étage

analyse spectrale # spectroscopie # fonction caractéristique # valeur propre # opérateur intégral de Fourier # géométrie complexe # métrique de Kähler-Einstein # torsion analytique # estimation de Strichartz

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Geometry and analysis of locally symmetric spaces of infinite volume Ji, Lizhen | CIRM H

Multi angle

Research talks;Algebraic and Complex Geometry

For any symmetric space $X$ of noncompact type, its quotients by torsion-free discrete isometry groups $\Gamma$ are locally symmetric spaces. One problem is to understand the geometry and analysis, especially the spectral theory, and interaction between them of such spaces. Two classes of infinite groups $\Gamma$ have been extensively studied:
$(1) \Gamma$ is a lattice, and hence $\Gamma$ $\backslash$ $X$ has finite volume.
$(2) X$ is of rank $1$, for example, when $X$ is the real hyperbolic space, $\Gamma$ is geometrically finite and $\Gamma$ $\backslash$ $X$ has infinite volume.
When $\Gamma$ is a nonuniform lattice in case $(1)$ or any group in case $(2)$, compactification of $\Gamma$ $\backslash$ $X$ and its boundary play an important role in the geometric scattering theory of $\Gamma$ $\backslash$ $X$. When $X$ is of rank at least $2$, quotients of $X$ of finite volume have also been extensively studied. There has been a lot of recent interest and work to understand quotients $\Gamma$ $\backslash$ $X$ of infinite volume. For example, there are some generalizations of convex cocompact groups, but no generalizations yet of geometrically finite groups. They are related to the notion of thin groups. One naturally expects that these locally symmetric spaces should have real analytic compactifications with corners (with codimension equal to the rank), and their boundary should also be used to parametrize the continuous spectrum and to understand the geometrically scattering theory. These compactifications also provide a natural class of manifolds with corners. In this talk, I will describe some questions, open problems and results.
For any symmetric space $X$ of noncompact type, its quotients by torsion-free discrete isometry groups $\Gamma$ are locally symmetric spaces. One problem is to understand the geometry and analysis, especially the spectral theory, and interaction between them of such spaces. Two classes of infinite groups $\Gamma$ have been extensively studied:
$(1) \Gamma$ is a lattice, and hence $\Gamma$ $\backslash$ $X$ has finite volume.
$(2) X$ is of rank ...

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The asymptotic spectral gap of hyperbolic dynamics : tentative to improve the estimates Faure, Frédéric | CIRM H

Multi angle

Research talks;Partial Differential Equations;Dynamical Systems and Ordinary Differential Equations;Mathematical Physics

Hyperbolic (Anosov or Axiom A) flows have discrete Ruelle spectrum. For contact Anosov flows, e.g. geodesic flows, where a smooth contact one form is preserved, the trapped set is a smooth symplectic manifold, normally hyperbolic, and M. Tsujii, S. Nonnenmacher and M. Zworski, have given an estimate for the asymptotic spectral gap, i.e. that appears in the limit of high frequencies in the flow direction. We will propose a different approach that may improve this estimate. This will be presented on a simple toy model, partially expanding maps. Work with Tobias Weich. Hyperbolic (Anosov or Axiom A) flows have discrete Ruelle spectrum. For contact Anosov flows, e.g. geodesic flows, where a smooth contact one form is preserved, the trapped set is a smooth symplectic manifold, normally hyperbolic, and M. Tsujii, S. Nonnenmacher and M. Zworski, have given an estimate for the asymptotic spectral gap, i.e. that appears in the limit of high frequencies in the flow direction. We will propose a different approach that ...

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Resonance chains on Schottky surfaces Weich, Tobias | CIRM H

Multi angle

Research talks;Partial Differential Equations;Dynamical Systems and Ordinary Differential Equations;Mathematical Physics

Recently David Borthwick discovered through numerical calculations surprising chain structures in the resonance spectrum of certain Schottky surfaces. In this talk we will see that theses resonance chains have the same origin as the resonance chains in the classical and quantum mechanical spectrum of the three disk system and we will see that they are related to a clustering in the length spectrum. Finally the existence of these chains will be proven for three funneled Schottky surfaces in a certain geometrical limit in the Teichmüller space. Joint work with S. Barkhofen and F. Faure. Recently David Borthwick discovered through numerical calculations surprising chain structures in the resonance spectrum of certain Schottky surfaces. In this talk we will see that theses resonance chains have the same origin as the resonance chains in the classical and quantum mechanical spectrum of the three disk system and we will see that they are related to a clustering in the length spectrum. Finally the existence of these chains will be ...

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Nodal lines and domains for Eisenstein series on surfaces Naud, Frédéric | CIRM H

Multi angle

Research talks;Partial Differential Equations;Dynamical Systems and Ordinary Differential Equations;Algebraic and Complex Geometry

Eisenstein series are the natural analog of ”plane waves” for hyperbolic manifolds of infinite volume. These non-$L^2$ eigenfunctions of the Laplacian parametrize the continuous spectrum. In this talk we will discuss the structure of nodal sets and domains for surfaces. Upper and lower bounds on the number of intersections of nodal lines with ”generic” real analytic curves will be given, together with similar bounds on the number of nodal domains inside the convex core. The results are based on equidistribution theorems for restriction of Eisenstein series to curves that bear some similarity with the so-called ”QER” results for compact manifolds. Eisenstein series are the natural analog of ”plane waves” for hyperbolic manifolds of infinite volume. These non-$L^2$ eigenfunctions of the Laplacian parametrize the continuous spectrum. In this talk we will discuss the structure of nodal sets and domains for surfaces. Upper and lower bounds on the number of intersections of nodal lines with ”generic” real analytic curves will be given, together with similar bounds on the number of nodal ...

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Hyperbolic triangles with no positive Neumann eigenvalues Judge, Christopher | CIRM H

Multi angle

Research talks;Analysis and its Applications;Partial Differential Equations;Dynamical Systems and Ordinary Differential Equations;Geometry

In joint work with Luc Hillairet, we show that the Laplacian associated with the generic finite area triangle in hyperbolic plane with one vertex of angle zero has no positive Neumann eigenvalues. This is the first evidence for the Phillips-Sarnak philosophy that does not depend on a multiplicity hypothesis. The proof is based an a method that we call asymptotic separation of variables.

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Extending the Cheeger-Müller theorem through degeneration Albin, Pierre | CIRM H

Multi angle

Research talks;Partial Differential Equations;Geometry;Topology

Reidemeister torsion was the first topological invariant that could distinguish between spaces which were homotopy equivalent but not homeomorphic. The Cheeger-Müller theorem established that the Reidemeister torsion of a closed manifold can be computed analytically. I will report on joint work with Frédéric Rochon and David Sher on finding a topological expression for the analytic torsion of a manifold with fibered cusp ends. Examples of these manifolds include most locally symmetric spaces of rank one. We establish our theorem by controlling the behavior of analytic torsion as a space degenerates to form hyperbolic cusp ends. Reidemeister torsion was the first topological invariant that could distinguish between spaces which were homotopy equivalent but not homeomorphic. The Cheeger-Müller theorem established that the Reidemeister torsion of a closed manifold can be computed analytically. I will report on joint work with Frédéric Rochon and David Sher on finding a topological expression for the analytic torsion of a manifold with fibered cusp ends. Examples of these ...

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On the Hodge-Kodaira Laplacian on the canonical bundle of a compact Hermitian complex space Bei, Francesco | CIRM H

Multi angle

Research talks;Geometry;Topology

Hermitian complex spaces are a large class of singular spaces that include for instance projective varieties endowed with the metric induced by the Fubini-Study metric. Many of the problems raised by Cheeger, Goresky and MacPherson in the case of complex projective varieties admit a natural extension also in this setting. The aim of this talk is to report about some recent results concerning the Hodge-Kodaira Laplacian acting on the canonical bundle of a compact Hermitian complex space. More precisely let $(X,h)$ be a compact and irreducible Hermitian complex space of complex dimension $m$. Consider the Dolbeault operator $\bar{\partial}_{m,0}$ : $L^2 \Omega^{m,0}(reg(X),h) \to L^2\Omega^{m,1}(reg(X),h)$ with domain $\Omega{_c^{m,0}}(reg(X))$ and let $\bar{\mathfrak{d}}_{m,0} : L^2 \Omega^{m,0}(reg(X),h)\to L^2\Omega^{m,1}(reg(X),h)$ be any of its closed extension. Now consider the associated Hodge-Kodaira Laplacian $\bar{\mathfrak{d}^*} \circ\bar{\mathfrak{d}}_{m,0}$ : $L^2 \Omega^{m,0}(reg(X),h)\to L^2\Omega^{m,0}(reg(X),h)$. We will show that the latter operator is discrete and we will provide an estimate for the growth of its eigenvalues. Finally we will prove some discreteness results for the Hodge-Dolbeault operator in the setting of both isolated singularities and complex projective surfaces (without assumptions on the singularities in the latter case). Hermitian complex spaces are a large class of singular spaces that include for instance projective varieties endowed with the metric induced by the Fubini-Study metric. Many of the problems raised by Cheeger, Goresky and MacPherson in the case of complex projective varieties admit a natural extension also in this setting. The aim of this talk is to report about some recent results concerning the Hodge-Kodaira Laplacian acting on the canonical ...

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