2025/2026

Algebraic Groups and Their Invariants 2

Type: Optional course (faculty)

Delivered by: Faculty of Mathematics

When: 1, 2 module

Open to: students of one campus

Instructors: Vladimir Zhgoon

Language: English

Contact hours: 60

Course Syllabus

Abstract

Geometric and classical invariant theory of algebraic groups is very important branch of modern mathematics. The first examples of invariants of linear transformations, such as the determinant, trace, and characteristic polynomial, are already encountered in the first year of linear algebra. Classical invariant theory is devoted to the description of the algebra of invariants of classical groups, such as the complete linear group, orthogonal and symplectic group. In turn, the geometric theory of invariants, which originates in the works of Hilbert and Mumford, is devoted to the study of the geometric properties of invariants, for example, the construction and study of the geometry of various quotient spaces, and is the main tool for constructing spaces of modules (curves, vector spaces and other objects). In this course, we will cover both classical invariant theory and geometric theory. We will also study equivariant embeddings of homogeneous spaces.