An introduction to Algebraic Groups and the Theory of Invariants

2024/2025

Academic Year

ENG

Instruction in English

6

ECTS credits

Delivered at:

Faculty of Mathematics

Course type:

Optional course (faculty)

When:

3, 4 module

Instructor

Zhgoon, Vladimir

Course Syllabus

Abstract

Geometric invariant theory and the classical theory of invariants of algebraic groups are a very important branchs of modern mathematics. Everyone meets already the first examples of invariants of linear transformations, such as determinant, trace, characteristic polynomial, already in the first course of linear algebra. The classical theory of invariants is devoted to the description of the algebra of polynomial or tenzor invariants of classical groups, such as the full linear group, orthogonal and symplectic groups. In turn, the geometric invariant theory, 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 the study of the geometry of various quotient spaces, and is use as the main tool for constructing moduli spaces (curves, vector spaces, and other objects). In the course we will touch on both the classical theory of invariants and geometric. We will also study equivariant embeddings of homogeneous spaces.