Frontiers in Number Theory, Physics, and Geometry I, Softcover reprint of hardcover 1st ed. 2006 On Random Matrices, Zeta Functions, and Dynamical Systems
Langue : Français
Coordonnateurs : Cartier Pierre E., Julia Bernard, Moussa Pierre, Vanhove Pierre
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.
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.
Very distinguished international list of authors including Fields Medaillists Alain Connes and Jean-Christophe Yoccoz Cutting-edge research in well-written expository form Includes supplementary material: sn.pub/extras
Date de parution : 02-2010
Ouvrage de 624 p.
15.5x23.5 cm
Date de parution : 12-2005
Ouvrage de 624 p.
15.5x23.5 cm
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