Olga Aryasova (Inst. of Geophysics, Nat. Acad. of Sciences of Ukraine / Friedrich–Schiller–Univ. Jena)
Rosa Preiss (TU Berlin)
This talk is based on a joint paper with Yvain Bruned, Ilya Chevyrev and Peter Friz. There, we revisit (higher-order) translation operators on rough paths, in both the geometric and branched setting. As in Hairer's work on the renormalization of singular SPDEs we propose a purely algebraic view on the matter. Recent advances in the theory of
regularity structures, especially the Hopf algebraic interplay of positive and negative renormalization of Bruned-Hairer-Zambotti (2016), are seen to have precise counterparts in the rough path context.
In this talk however, I will focus on the context of branched rough paths and branched rough differential equations. If time permits, I will conclude with a short outlook to the link with renormalization in regularity structures.