2025/2026
An Introduction to Elliptic Operators and Index Theorems
Type:
Optional course (faculty)
Delivered by:
Faculty of Mathematics
When:
1, 2 module
Open to:
students of all HSE University campuses
Instructors:
Alexei Gorinov
Language:
English
Contact hours:
60
Course Syllabus
Abstract
In this seminar we will cover the basics of the theory of elliptic operators, examples of which include the de Rham and Dolbeault operators, as well as their generalisations such as the Dirac operator. We will explain how several seemingly unrelated results in geometry and topology (e.g. the Hirzebruch and Rokhlin signature theorems and the Riemann\Ч Roch theorem) all follow from the general index formula by M.~Atiyah and I.~Singer, and sketch a proof of the latter.