题 目： Integro-differential Algebras and Groebner-Shirshov Bases
报 告 人：Prof.Li Guo, Rutgers University and Lanzhou University
Abstract: The concept of an integro-differential algebra is an algebraic abstraction of calculus. The axioms of the abstraction consist of the differential operator (derivation) with the Leibniz rule, the integral operator with the integral by parts formula and the First Fundamental Theorem of Calculus. Such an algebraic structure plays an essential role in the study of boundary value problems of differential equations. We discuss a construction of free integro-differential algebras by the method of Groebner-Shirshov bases, built on the constructions of free objects in the categories of differential algebras, Rota-Baxter algebras and differential Rota-Baxter algebras.
This talk is based on joint works with X. Gao, G. Regensburger, M. Rosenkranz and S. Zhang.