From Number Theory to Physics

Various developments in physics have involved many questions related to number theory, in an increasingly direct way. This trend is especially visible in two broad families of problems, namely, field theories, and dynamical systems and chaos. The 14 chapters of this book are extended, self-contained versions of expository lecture courses given at a school on "Number Theory and Physics" held at Les Houches for mathematicians and physicists. Most go as far as recent developments in the field. Some adapt an original pedagogical viewpoint.

An Introduction to Zeta Functions	p. 1
Introduction to Compact Riemann Surfaces, Jacobians, and Abelian Varieties	p. 64
Elliptic Curves	p. 212
Introduction to Modular Forms	p. 238
Decorated Elliptic Curves: Modular Aspects	p. 292
Galois Theory, Algebraic Number Theory, and Zeta Functions	p. 313
Galois Theory for Coverings and Riemann Surfaces	p. 394
Differential Galois Theory	p. 413
p-adic Numbers and Ultrametricity	p. 440
Introduction to Lattice Geometry	p. 476
A Short Introduction to Quasicrystallography	p. 496
Gap Labelling Theorems for Schrodinger Operators	p. 538
Circle Maps: Irrationally Winding	p. 631
An Introduction to Small Divisors Problems	p. 659
Index	p. 680
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From Number Theory to Physics

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