Hopf algebras, rough paths and
regularity structures
报告专家：高兴（兰州大学）
报告时间：2024年12月9日（星期一)下午4:00-5:00
报告地点：国家天元西南数学中心516
报告摘要：Rough paths have been introduced by T. Lyons in 1998 as a new tool for solving rough differential equations. They are built from substitutes of Chen's iterated integrals of a path when this path is α-Holder-continuous with 0<α≤1. A milestone result of rough paths is that Hairer employed rough path theory to solve the KPZ equation, obtaining the expected solution of physicists.
Later Hairer generalized rough paths to regularity structures, with the goal to solve stochastic partial differential equations. Quite recently, Otto gave a diagram-free approach to the stochastic estimates in regularity structures, based on multi-indexes.
In this talk, I will introduce (combinatorial) Hopf algebras towards applications to rough paths and regularity structures. In particular, a Hopf algebraic framework of multi-index rough paths is exposed.
专家简介：高兴，博士，兰州大学教授、博士生导师、萃英学者、甘肃省陇原人才，于2010年7月在兰州大学数学与统计学院获得博士学位，留校工作至今。主要从事Rota-Baxter代数和代数组合等领域的研究，发表SCI学术论文六十余篇。主持数学天元基金、青年科学基金、国家自然科学基金面上项目和甘肃省自然科学基金项目, 获甘肃省自然科学奖二等奖，出版教材一本。
邀请人：张斌
