Algebraic Groups and Their Invariants 2

2025/2026

Учебный год

ENG

Обучение ведется на английском языке

6

Кредиты

Лучший по критерию «Полезность курса для расширения кругозора и разностороннего развития»

Лучший по критерию «Новизна полученных знаний»

Кто читает:

Факультет математики

Статус:

Дисциплина общефакультетского пула

Когда читается:

1, 2 модуль

Преподаватель

Жгун Владимир Сергеевич

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.