The theory of standard bases of Gröbner–Shirshov is a beautiful branch of algebra that originated in the 50s/60s of the last century and received a powerful development thanks to computer algebra systems. The classical application of standard bases is an algorithm for solving systems of nonlinear algebraic equations, which is a far-reaching generalization of the classical Gauss method for excluding variables in systems of linear algebraic equations.

The aim of the course is to introduce students to standard bases and their application to solving systems of nonlinear algebraic equations, to constructing algebras with universal properties (for example, Grassmann algebra, tensor product of algebras, universal enveloping algebra), and to solve a number of other algorithmic questions.

The course will consist of 12-14 lectures.

Financial support. The course is supported by the Ministry of Science and Higher Education of the Russian Federation (the grant to the Steklov International Mathematical Center, Agreement no. 075-15-2019-1614).

Program

Lecturer
Kiselev Denis Dmitrievich

Institutions
Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
Steklov International Mathematical Center