Session A5 - Geometric Integration and Computational Mechanics
July 11, 17:00 ~ 17:30 - Room 111
ROUGH PATHS ON HOMOGENEOUS SPACES
Bergen, Norway - email@example.com
We consider rough paths in the context of differential equations on homogenous manifolds. Our approach generalises both the Chen-type shuffle algebra of word series underlying Terry Lyons’ theory of rough paths as well as the branched rough paths of Massimiliano Gubinelli, which are based on B-series and the Connes-Kreimer Hopf algebra of rooted trees. The new approach contains these as special cases and extends geometrically to rough paths evolving on homogeneous manifolds.
 K. T. Chen, Integration of paths, geometric invariants and a generalized Baker-Hausdorff formula, Ann. Math. 65 No1, 163–178 (1957).
 M. Gubinelli, Ramification of Rough Paths, Journal of Differential Equations 248, no. 4 (2010) 693-721.
 T. Lyons, Differential equations driven by rough signals, Rev. Mat. Iberoamericana 14 No2, 215–310 (1998).
Joint work with Charles Curry (NTNU, Norway), Kurusch Ebrahimi-Fard (NTNU, Norway) and Dominique Manchon (Clermont-Ferrand, France).