Many years ago, Rota proposed a program on determining algebraic identities that can be satisfied by linear operators. After an extended period of dormant, progress on this program picked up speed in recent years, thanks to perspectives from operated algebras and Groebner-Shirshov bases. These advances were achieved in a series of papers from special cases to more general situations. These perspectives also indicate 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 to the applications of rewriting systems and Groebner-Shirshov bases. Open problems, old and new, will also be proposed. This is a joint work with Xing Gao, Huhu Zhang and several other authors.

会议密码：1125