Ergodic Theory: From Spectral Methods to Entropy
This course provides a rigorous foundation in ergodic theory, following the textbook An Introduction to Ergodic Theory by Peter Walters. It covers the fundamental principles of measure-preserving transformations, spectral methods entropy, and their interplay with topological dynamics. The curriculum emphasizes both theoretical development and illustrative examples, including shifts, group rotations, and endomorphisms.
Lecturer
Date
5th March ~ 21st May, 2026
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Thursday | 13:30 - 16:55 | A3-3-201 | ZOOM 14 | 712 322 9571 | BIMSA |
Prerequisite
Foundations of Measure Theory
Syllabus
1.Preliminaries
2.Measure-Preserving Transformations
3.Isomorphism and Conjugacy
4.Discrete Spectrum
5.Entropy
6.Topological Dynamics and
7.Invariant Measures
8.Topological Entropy
2.Measure-Preserving Transformations
3.Isomorphism and Conjugacy
4.Discrete Spectrum
5.Entropy
6.Topological Dynamics and
7.Invariant Measures
8.Topological Entropy
Audience
Advanced Undergraduate
, Graduate
Video Public
Yes
Notes Public
No
Language
Chinese
Lecturer Intro
Sixu Liu received her Ph.D. degree from Peking University in 2019. She then worked as a postdoc at Tsinghua University before joining BIMSA as an assistant professor in 2022. Her main research interests include dynamical systems and ergodic theory, as well as statistical experimental design.