We review aspects of twistor theory, its aims and achievements spanning the last five
decades. In the twistor approach, space–time is secondary with events being derived …

During the past 30 years there have been important and far reaching developments in the
study of nonlinear waves including" soliton equations", a class of nonlinear wave equations …

Many of the familiar integrable systems of equations are symmetry reductions of self-duality
equations on a metric or on a Yang-Mills connection. For example, the Korteweg-de Vries …

We study various aspects of N= 2 critical strings. The most important aspect of these theories
is that they provide a consistent quantum theory of self-dual gravity in four dimensions. We …

We consider strings with an N= 2 local superconformal symmetry on the worldsheet. The
critical dimension for this theory is four (two complex dimensions) with the signature (2, 2). A …

The string equations of hermitian and unitary matrix models of 2 D gravity are flatness
conditions. These flatness conditions may be interpreted as the consistency conditions for …

The solutions of Einstein's equations admitting one non-null Killing vector field are best
studied with the projection formalism of Geroch. When the Killing vector is lightlike, the …

Geometry of the solution space of the self-dual Yang–Mills (SDYM) equations in Euclidean
four-dimensional space is studied. Combining the twistor and group-theoretic approaches …

The characteristic feature of the so‐called Painlevé test for integrability of an ordinary (or
partial) analytic differential equation, as usually carried out, is to determine whether all its …

Broadly speaking, twistor theory is a framework for encoding physical information on space-
time as geometric data on a complex projective space, known as a twistor space. The …