Infinite-dimensional Lie groups in renormalisation and regularity structures

20.10.2017, 11:00 Uhr  –  Haus 9, Raum 2.22
Arbeitsgruppenseminar Analysis

Alexander Schmeding (TU Berlin)

In the theory of renormalisation of quantum field theories (Connes and Kreimer) and in Hairer's regularity structures for stochastic differential equations certain "renormalisation groups" appear.
These encode part of the renormalisation process and typically turn
out to be character groups of Hopf algebras which encode the combinatorics of renormalisation.
Recently, we have uncovered that these groups are in a natural way infinite-dimensional Lie groups.

In this talk I will give an introduction to this topic together with a scenic tour to some main examples. As we will review the basic concepts (calculus beyond Banach spaces, infinite dimensional Lie groups) no prior knowledge about infinite-dimensional geometry is required to follow the talk.