报告名称：Rota's Program on Algebraic Operators

报告专家：高兴

专家所在单位：兰州大学

报告时间：2021年6月24日15:00-17:00

报告地点：腾讯会议（会议ID：191828490）

专家简介：高兴，博士，兰州大学“萃英学者”、教授，博士生导师。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。在2015年8月至2016年8月间，在美国Rutgers大学交流访问。主要从事Rota-Baxter代数和代数组合等领域的研究， 在Journal of Algebra、 Journal of Pure and Applied Algebra、J.Algebraic Combin. 等国际期刊上发表SCI学术论文四十余篇。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。

报告摘要：Many years ago, Rota proposed a program on determining algebraic identities that can be satisfied by linear operators. After an extended period of dormant, advancement on this program picked up speed in recent years, thanks to progresses on operated algebras and Gr\"obner-Shirshov bases. The advancement was achieved in a series of papers from special cases to more general situations. This progresses show that Rota's insight can be manifested very broadly, for other algebraic structures such as Lie algebras, and further in the context of operads. This talk gives a survey on the motivation, early developments and recent advances on Rota's program, for linear operators on associative algebras and Lie algebras. Emphasis will be given on the applications of rewriting systems and Gr\"obner-Shirshov bases.

邀请人：刘合国

（审稿：郑大彬）