Thermodynamic Formalism: Applications to Probability, Geometry and Fractals

Thermodynamic formalism is an area of dynamical systems which originated in the 1960s and 1970s with the introduction of ideas of mathematical physics.  In the past few years it has undergone something of a renaissance with applications to many different areas, including Riemannian geometry, microlocal analysis, and analytic number theory.  This is an active area of research which has both intrinsic elegance and useful applications to neighbouring areas.