Workshop

**Renormalisation from Quantum Field Theory to Random and Dynamical Systems**

6.11.2013 – 8.11.2013

The meeting aims at investigating the uses of renormalisation techniques inspired from physics beyond their original field of application, namely beyond quantum field theory. The need to renormalise arises in many a field such as in the theory of random PDEs and dynamical systems and in various disguises. Solving PDEs with singular (typically random) input or local dynamical systems via a linearisation procedure, involves taking limits of regularised expressions modified by the addition of diverging counterterms in order to ensure a convergence. These counterterms arise naturally through the action of a "renormalisation group", a concept borrowed from quantum field theory. The work of Dirk Kreimer and Alain Connes who gave an algebraic reformulation in the context of Hopf algebras, of the forest formula used by physicists, provides algebraic tools to organise the counterterms by means of a Birkhoff-Hopf factorisation. This algebraic approach to issues of an a priori purely analytic nature was the source of inspiration for further developments on the tree structure underlying the combinatorics of Feynman diagrams. This meeting, which aims at providing an insight on the interaction between purely analytic renormalisation issues and the algebraic constructions used to approach them, is organised around the following topics:

Confirmed Speakers:

• Viet Dang Nguyen, Paris VI Renormalised products of distributions which fail to satisfy the Hörmander condition

• Loïc Foissy, Reims Algebraic and combinatorial aspects of quantum field theory

• Massimiliano Gubinelli, Paris Dauphine Paracontrolled distributions

• Peter Imkeller, H.U. Berlin A Fourier analytic approach to rough paths

• Dominique Manchon, Clermont-Ferrand The double shuffle structure of the Ohno-Okuda-Zudilin q-multiple zeta values

• Frédéric Menous, Paris XI, Orsay Renormalization and dynamical systems

• Erik Panzer, H.U. Berlin Renormalization by kinematic subtraction and Hopf algebras

• Nicolas Perkowski, H.U. Berlin Paracontrolled distributions and the parabolic Anderson model

• Hendrik Weber, University of Warwick Non-linear SPDEs, controlled distributions and renormalisation

Participants are welcome to attend a COLLOQIUM on topics related to those of the meeting.

Please register on line via the following link before Sept. 20th:

http://analysis.math.uni-potsdam.de/isw/InternationalScientificWorkshop.html