Mathematical physics spans a wide range of topics in theoretical physics, from almost pure mathematics to some studies which can be related to experiments. Despite this variety, many of these topics are connected by the fact that they use common mathematical and theoretical tools (quantum field theory, integrable systems, conformal field theory, string theory, random matrices, combinatorics, probability and random processes), and that mathematical rigor and consistency, and the obtention of precise and often explicit results, are very important.
Many of these tools have been developed over the years at IPhT. On several subjects, contacts and collaborations between IPhT and mathematicians develop quickly. This does not reflect a move towards more abstraction, but a genuine interest of mathematicians for problems from physics, and of physicsts for the ideas and the new mathematical tools developped by mathematicians. Mathematical physics at IPhT also has close contacts with statistical physics and high energy physics. For instance, important progress are made on the problem of evaluating scattering amplitudes, which is now finding its way in LHC phenomenology, in cosmology and in statistical physics.