More than 65 years ago, John Wheeler suggested that quantum uncertainties of the metric
would be of order one at the Planck scale, leading to large fluctuations in spacetime …

Advances in mathematics and physics have often occurred together. The development of
Newton's theory of mechanics and the simultaneous development of the techniques of …

A bstract We consider the twistor description of classical self-dual Einstein gravity in the
presence of a defect operator wrapping a certain ℂℙ 1. The backreaction of this defect …

Einstein's equations stem from General Relativity. In the context of Riemannian manifolds,
an independent mathematical theory has developed around them. Recently, it has produced …

The book starts with a thorough introduction to connections and holonomy groups, and to
Riemannian, complex and Kähler geometry. Then the Calabi conjecture is proved and used …

Effective field theories in type I and II superstring theories for D-branes located at points in
the orbifold C^ 2/Z_n are supersymmetric gauge theories whose field content is conveniently …

According to the definition given by Calabi [4], a Riemannian manifold (X, g) is hyper-Kahler
if it is equipped with three automorphisms J, J, K of the tangent bundle which satisfy the …

We classify the action of one parameter isometry groups of Gravitational Instantons,
complete non singular positive definite solutions of the Einstein equations with or without Λ …

In 438 alphabetically-arranged essays, this work provides a useful overview of the core
mathematical background for nonlinear science, as well as its applications to key problems …

A complete geometrical classification of supersymmetric σ-models is given. Extended
supersymmetry requires covariantly constant complex structures, and Kahler and …