应兰州大学数学与统计学院、萃英学院邀请，法国国家科学研究中心 Dominique Manchon 研究员将于2025年9月1日---13日访问我校，并进行线下学术报告。

报告题目：Combinatorial Hopf algebras and rough paths (I)

时间：9月4日（周四）14：30

地点：榆中校区致远楼 912

报告摘要：After a quick reminder on groups, I will introduce the notion of Hopf algebra and give two important examples: the shuffle Hopf algebra and the Butcher-Connes-Kreimer Hopf algebra of rooted forests. Other Hopf algebras will be briefly mentioned if time permits: the Munthe-Kaas - Wright Hopf algebra of planar rooted forests, and the Hopf algebra of multi-indices. Some interesting non-associative algebraic structure will show up in the presentation: pre-Lie algebras, post-Lie algebras and Novikov algebras. After a quick presentation of Chen's iterated integrals and their relation to the shuffle Hopf algebra, I will introduce rough paths, and show how this notion can be adapted to any commutative connected graded Hopf algebra. Finally, and if time permits, I also will introduce the important notion of controlled path driven by a rough path.

欢迎广大师生光临!

报告人简介

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.

数学与统计学院

萃英学院

2025年8月29日