Speaker：Xing Gao（Lanzhou University）

Time：2022-10-27, 14:30

Location：Tencent Meeting ID：384 248 327（No Password）

Abstract:

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.