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Course Syllabus

2024/2025

Dynamics of Automorphisms of Algebraic Varieties

Type: Optional course (faculty)
Delivered by: Faculty of Mathematics
Where: Faculty of Mathematics
When: 1, 2 module
Open to: students of all HSE University campuses
Language: English
ECTS credits: 3
Contact hours: 30

Course Syllabus

Abstract

Group of automorphisms of an algebraic variety is an important invariant, geometric properties of the variety depend a lot on it. In this course we are going to discuss positive entropy automorphisms. By Gromov-Yomdin's theorem the entropy of an automorphism can be computed with algebraic geometry invariants. We are going to study the connection of the dynamics and the geometry of regular and birational automorphisms of varieties, to describe properties of a very general element of the Cremona group, and discuss the behavior of families of birational automorphisms.