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After an introduction to the hyperbolic geometry of surfaces, with a special emphasis on those of arithmetic type, and then an introduction to spectral analytic methods on the Laplace operator on these surfaces, the author develops the analogy between geometry (closed geodesics) and arithmetic (prime numbers) in proving the Selberg trace formula. Along with important number theoretic applications, the author exhibits applications of these tools to the spectral statistics of the Laplacian and the quantum unique ergodicity property. The latter refers to the arithmetic quantum unique ergodicity theorem, recently proved by Elon Lindenstrauss.
The fruit of several graduate level courses at Orsay and Jussieu, The Spectrum of Hyperbolic Surfaces allows the reader to review an array of classical results and then to be led towards very active areas in modern mathematics.
After an introduction to the hyperbolic geometry of surfaces, with a special emphasis on those of arithmetic type, and then an introduction to spectral analytic methods on the Laplace operator on these surfaces, the author develops the analogy between geometry (closed geodesics) and arithmetic (prime numbers) in proving the Selberg trace formula. Along with important number theoretic applications, the author exhibits applications of these tools to the spectral statistics of the Laplacian and the quantum unique ergodicity property. The latter refers to the arithmetic quantum unique ergodicity theorem, recently proved by Elon Lindenstrauss.
The fruit of several graduate level courses at Orsay and Jussieu, The Spectrum of Hyperbolic Surfaces allows the reader to review an array of classical results and then to be led towards very active areas in modern mathematics.
Nicolas Bergeron is a Professor at Université Pierre et Marie Curie in Paris. His research interests are in geometry and automorphic forms, in particular the topology and spectral geometry of locally symmetric spaces.
Features profound and recent results of the spectral theory of automorphic surfaces
Provides a self-contained proof of the so-called Jacquet-Langlands correspondence
Includes an introduction to Lindenstrauss's ergodic theoretic proof of quantum unique ergodicity for compact arithmetic surfaces, for which he was awarded a Fields medal in 2010
Includes supplementary material: [...]
| Erscheinungsjahr: | 2016 |
|---|---|
| Fachbereich: | Geometrie |
| Genre: | Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Taschenbuch |
| Seiten: | 388 |
| Reihe: | Universitext |
| Inhalt: |
xiii
370 S. 8 farbige Illustr. 370 p. 8 illus. in color. |
| ISBN-13: | 9783319276649 |
| ISBN-10: | 3319276646 |
| Sprache: | Englisch |
| Herstellernummer: | 978-3-319-27664-9 |
| Ausstattung / Beilage: | Paperback |
| Einband: | Kartoniert / Broschiert |
| Autor: | Bergeron, Nicolas |
| Auflage: | 1st ed. 2016 |
| Hersteller: |
Springer International Publishing
Universitext |
| Maße: | 235 x 155 x 20 mm |
| Von/Mit: | Nicolas Bergeron |
| Erscheinungsdatum: | 02.03.2016 |
| Gewicht: | 0,657 kg |
Nicolas Bergeron is a Professor at Université Pierre et Marie Curie in Paris. His research interests are in geometry and automorphic forms, in particular the topology and spectral geometry of locally symmetric spaces.
Features profound and recent results of the spectral theory of automorphic surfaces
Provides a self-contained proof of the so-called Jacquet-Langlands correspondence
Includes an introduction to Lindenstrauss's ergodic theoretic proof of quantum unique ergodicity for compact arithmetic surfaces, for which he was awarded a Fields medal in 2010
Includes supplementary material: [...]
| Erscheinungsjahr: | 2016 |
|---|---|
| Fachbereich: | Geometrie |
| Genre: | Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Taschenbuch |
| Seiten: | 388 |
| Reihe: | Universitext |
| Inhalt: |
xiii
370 S. 8 farbige Illustr. 370 p. 8 illus. in color. |
| ISBN-13: | 9783319276649 |
| ISBN-10: | 3319276646 |
| Sprache: | Englisch |
| Herstellernummer: | 978-3-319-27664-9 |
| Ausstattung / Beilage: | Paperback |
| Einband: | Kartoniert / Broschiert |
| Autor: | Bergeron, Nicolas |
| Auflage: | 1st ed. 2016 |
| Hersteller: |
Springer International Publishing
Universitext |
| Maße: | 235 x 155 x 20 mm |
| Von/Mit: | Nicolas Bergeron |
| Erscheinungsdatum: | 02.03.2016 |
| Gewicht: | 0,657 kg |
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