'Loop quantum gravity, twisted geometries and twistors'

Abstract: Loop quantum gravity is a background-independent approach to the
quantization of general relativity. While the theory is continuous at
the fundamental level, it is often useful to consider a truncation
thereof, defined on the lattice dual to a graph. This truncation
captures a finite number of degrees of freedom, which have been shown
to describe a certain generalization of Regge geometries, called
twisted geometries.  In this talk, I will give a brief overview of the
theory and its geometric interpretation. Then, I will describe how
these discrete geometries can be described in terms of a collection of
twistors associated to the lattice, thus providing a new sense in
which twistors can be seen as non-linear gravitons.  Finally, I will
discuss the present state of the art concerning the dynamics and the
continuum limit.