题    目：Combinatorial Hopf algebras and rough paths

主讲人：Dominique Manchon 研究员

单    位：法国国家科学研究中心

时    间：2025年9月8日 15:00

地    点：学院南阶梯教室

摘    要：K. T. Chen’s iterated can be used to define the signature of a smooth path. Rough paths were introduced by T. Lyons as substitutes of the signature when the path is not differentiable. The shuffle Hopf algebra is a key part of the algebraic structure behind. We shall define rough paths associated to a broad class of combinatorial Hopf algebras, including the Connes-Kreimer Hopf algebra of rooted forests (branched rough paths), the Munthe-Kaas - Wright Hopf algebra (planarly branched rough paths), and the multi-index Hopf algebra (multi-index rough paths). Relations between these different versions will be discussed. If time permits, the corresponding notion of controlled rough path will also be addressed.

简    介：Dominique Manchon is Chargé de Recherches (senior researcher) at CNRS, Laboratoire de Mathématiques Blaise Pascal Université Clermont-Auvergne (France). His main research interests are representation theory, algebra and algebraic combinatorics including applications to analysis, in particular rough path theory. He has been invited researcher in Bergen University (Norway), NTNU (Trondheim, Norway), Erwin Schrödinger Institut (Vienna, Austria) and ICMAT (Madrid, Spain). He has been giving lectures and research talks in numerous international conferences and schools in France as well as abroad, in several countries including Tunisia, Norway, Spain, Germany, Austria, Italy, Great Britain, Iceland, Sweden, Denmark, Columbia, Venezuela, Chile and Ivory Coast. His scientific production (more than 50 articles) deals with representation theory of nilpotent Lie groups, deformation quantization and algebra. Combinatorial Hopf algebras, operads and related non-associative strutures (pre-Lie algebras, post-Lie algebras,...), together with their interactions with analysis and geometry, have become his main research topics in the two last decades.