Information and Geometry

The geometry of information finds wide applications in areas ranging from simple day to day thermodynamical systems to space-time singularities called black holes. The latter can be related to strongly coupled quantum field theories via the so called gauge-gravity duality. Current progress indicates that one can in principle address all these issues in a unifying framework. In this talk, we will discuss some important recent developments in the subject. We start from information in basic thermodynamics, comment on this in the context of statistical mechanics and field theories, and end with a recent conjecture by Susskind that black holes might be examples of the fastest computers.