Introduces the classical theory of complex tori and abelian varieties, presenting modern aspects of complex algebraic and analytic geometry. Beginning with complex elliptic curves, this textbook moves on to the higher-dimensional case, giving characterizat

Hodge theory originated as an application of harmonic theory to the study of the geometry of compact complex manifolds. The ideas have proved to be quite powerful, leading to fundamentally important results throughout algebraic geometry.

A fundamental element of the study of 3-manifolds is Thurston's remarkable geometrization conjecture, which states that the interior of every compact 3-manifold has a canonical decomposition into pieces that have geometric structures. In most cases, these structures are complete metrics of constant negative curvature, that is to say, they are hyperbolic manifolds. The conjecture has been proved in some important cases, such as Haken manifolds and certain types of fibered manifolds. The influence of Thurston's hyperbolization theorem on the geometry and topology of 3-manifolds has been...

The purpose of thermodynamics and statistical physics is to understand the equilibrium of a gas or the different states of matter. To understand the strange fractal sets appearing when one iterates a quadratic polynomial is one of the goals of the theory of holomorphic dynamical systems. These two theories are strongly linked: the laws of thermodynamics happen to be an extremely powerful tool for understanding the objects of holomorphic dynamical systems. A thermodynamic formalism has been developed, bringing together notions that are a priori unrelated. While the deep reasons of this...