2024/2025
An introduction to Algebraic Groups and the Theory of Invariants
Type:
Optional course (faculty)
Delivered by:
Faculty of Mathematics
Where:
Faculty of Mathematics
When:
3, 4 module
Open to:
students of all HSE University campuses
Instructors:
Vladimir Zhgoon
Language:
English
ECTS credits:
6
Contact hours:
72
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.