Frontiers in Number Theory, Physics and Geometry - 1: Frontiers in Number Theory, Physics, and Geometry I

The relation between mathematics and physics has a long history, in which the role of number theory and of other more abstract parts of mathematics has recently become more prominent. More than 10 years after a first meeting between number theorists and physicists at the Centre de Physique des Houches, a second two-week event focused on the broader interface of number theory, geometry, and physics. This book collects the material presented at this meeting.

List of contents

Random Matrices: from Physics to Number Theory.- Quantum and Arithmetical Chaos.- Notes on L-functions and Random Matrix Theory.- Energy Level Statistics, Lattice Point Problems, and Almost Modular Functions.- Arithmetic Quantum Chaos of Maass Waveforms.- Large N Expansion for Normal and Complex Matrix Ensembles.- Symmetries Arising from Free Probability Theory.- Universality and Randomness for the Graphs and Metric Spaces.- Zeta Functions.- From Physics to Number Theory Via Noncommutative Geometry.- More Zeta Functions for the Riemann Zeros.- Hilbert Spaces of Entire Functions and Dirichlet L-Functions.- Dynamical Zeta Functions and Closed Orbits for Geodesic and Hyperbolic Flows.- Dynamical Systems: Interval Exchange, Flat Surfaces, and Small Divisors.- Continued Fraction Algorithms for Interval Exchange Maps: an Introduction.- Flat Surfaces.- Brjuno Numbers and Dynamical Systems.- Some Properties of Real and Complex Brjuno Functions.

Summary

The relation between mathematics and physics has a long history, in which the role of number theory and of other more abstract parts of mathematics has recently become more prominent. More than 10 years after a first meeting between number theorists and physicists at the Centre de Physique des Houches, a second two-week event focused on the broader interface of number theory, geometry, and physics. This book collects the material presented at this meeting.

Product details

• Authors: Michael Tehranchi
• Assisted by: Pierre Cartier (Editor), Pierre E. Cartier (Editor), Pierre Emile Cartier (Editor), Bernar Julia (Editor), Bernard Julia (Editor), Pierre Moussa (Editor), Pierre Moussa et al (Editor), Pierre Vanhove (Editor)
• Publisher: Springer, Berlin
• Languages: English
• Product format: Hardback
• Released: 28.12.2005
• EAN: 9783540231899
• ISBN: 978-3-540-23189-9
• No. of pages: 624
• Weight: 1036 g
• Illustrations: XII, 624 p.
• Sets: Frontiers in Number Theory, Physics and Geometry; Frontiers in Number Theory, Physics and Geometry
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Arithmetic, algebra; C, Mathematische Physik, Algebraische Geometrie, Mathematics and Statistics, Algebraic Geometry, Theoretical, Mathematical and Computational Physics, Number Theory, Mathematical physics, zeta functions