Weierstrass Institute
for Applied Analysis and Stochastics

Renormalisation techniques initiated by physicists in the context of quantum field theory to make sense of a priori divergent expressions, have since then been revisited, transposed and further developed by mathematicians in various disguises. Ideas borrowed from renormalisation have inspired mathematicians with very different domains of expertise and given new impulses in many a field such as analysis (with Ecalle’s theory of resurgence, resolution of singularities), algebra (Birkhoff-Hopf factorization, Rota-Baxter operators), differential geometry (quantum field theory on Lorentzian space-time), algebraic geometry (motives, multi-zeta values) and probability (regularity structures).

This profusion of approaches to and inspired from renormalisation techniques is propitious for fruitful potential interdisciplinary interactions, which this workshop aims at identifying and stimulating. It aims at bringing together mathematicians (algebraists, geometers and analysts) and physicists, who will present their work involving renormalisation, thus encouraging the dialogue between various communities using the concept of renormalisation.

A previous interdisciplinary meeting of this kind “Renormalisation from Quantum Field Theory to Random and Dynamical Systems” organized by two of the present coorganisers (D. Manchon, S. Paycha together with M. Högele) in Potsdam in November 2013, proved extremely successful in so far as it actually stimulated interactions between researchers from different communities, in particular between geometers, physicists and probabilists. Many participants expressed their enthusiasm for this rather unusually broad interdisciplinary meeting yet with enough common ground for fruitful interactions. Three years later, we feel that the time has come to organise another confrontation of ideas around renormalisation related issues, in the form of a meeting involving some of the participants of the previous one and new ones who can bring in yet another outlook on these issues.

The meeting will be organised around 4 mini-courses (3hrs each in total) in the mornings and 50 min talks in the afternoons. The mini-courses will serve as introductions to specific active research topics where renormalisation plays a central role.

Peter Friz (Technische Universität & Weierstrass Institut, Berlin)
Dominique Manchon (CNRS - Université Blaise Pascal, Clermont-Ferrand)
Sylvie Paycha (Universität Potsdam)