Renormalization is a set of techniques developed by theoretical physicists to deal with the appearance of divergent quantities in quantum field theory. Highly controversial because they were not mathematically rigorous, these techniques have become increasingly accepted since the work of K. Wilson in the 1970s, showing how they can be used to understand phase transition phenomena in statistical physics, followed by the famous article by J. Polchinski in 1984 on effective Lagrangians.
Although renormalization is now well accepted and understood in Physics, it remains a challenge to provide the appropriate mathematical theory that explains it.
In this talk, we will focus on the approach of R. Bauerschmidt and T. Bodineau. We will try to explain it through the continuum phi-4 model, then show how certain quantities such as mixing times can be studied along the flow, and finally how the flow can be used to construct Lipschitz transport maps.
