An Introduction to Ergodic Theory

Ergodic theory is the study of the qualitative properties of actions of groups on spaces. It is a very active area with many applications in physics, harmonic analysis, probability, and number theory. In this course, I will introduce some notations, examples about ergodicity, mixing, recurrence, ergodic decomposition, ergodic theorems,... More precisely, I am planning to teach

• Ergodicity, Recurrence, Mixing.
• Invariant Measures for Continuous Maps.
• Conditional Measures and Algebras. 
• Factors and Joinings. 
• Structure of Measure Preserving Systems. 
• Actions of Locally Compact Groups. 
• Geodesic Flow on Quotients of the Hyperbolic Plane (if time allowed).

Textbook
M. Einsiedler and T. Ward, Ergodic Theory with a view towards Number Theory, Graduate Texts in Mathematics, 259. Springer-Verlag London, Ltd., London, 2011.

Recommended reading

1. Furstenberg, H. Recurrence in ergodic theory and combinatorial number theory. M. B. Porter Lectures. Princeton University Press, Princeton, N.J., 1981. 
2. Glasner, Ergodic Theory via Joinings. American Mathematical Society, Providence, RI, 2003. 
3. Petersen, Ergodic theory. Corrected reprint of the 1983 original. Cambridge Studies in Advanced Mathematics, 2. Cambridge University Press, Cambridge, 1989.
4. Walters, An Introduction to Ergodic Theory. Graduate Texts in Mathematics, 79. Springer-Verlag, New York, Berlin, 1982.

Date and time info
Thursday 11.00 - 12.30

Keywords
Ergodic Theory, Recurrence, Mixing, Invariant Measures

Prerequisites
You should know basic Measure Theory and Functional Analysis

Language
English