Li Guo (Rutgers University)
Throughout the history, mathematical objects are often
understood through studying operators defined on them. Well-known
examples include Galois theory where a field is studied by its
automorphisms (the Galois group), and analysis and geometry where
functions and manifolds are studied through their derivations,
integrals and related vector fields.
A long time ago, Rota raised the question of identifying all the
identities that could be satisfied by a linear operator defined on
algebras. We will discuss some recent progress on understanding and
solving Rota's Problem by the methods of rewriting systems and
Groebner-Shirshov bases. This is joint work with Xing Gao, William
Sit, Ronghua Zhang and Shanghua Zheng.
