- Lecture 1: Spaces with measure (August 9).
- Lecture 2: Poincaré recurrence theorem (August 11).
- Lecture 3: Examples of ergodic measures (August 16).
- Lecture 4: Convex cone of measures and weak-* topology (August 18).
- Lecture 5: Weak-* topology and Birkhoff ergodic theorem (August 23).
- Lecture 6: Birkhoff ergodic theorem and Hopf Argument (October 4).
- Lecture 7: Von Neumann ergodic theorem and pseudo-Anosov maps (October 6).
- Lecture 8: Riemannian geometry of space forms (October 11).
- Lecture 9: Isomorphisms of low-dimensional Lie groups (October 13).
- Lecture 10: Conformal automorphisms of the disk (October 18).
- Lecture 11: Möbius group and geodesics of the Poincare metric (October 20).
- Lecture 12: Geodesic flow (October 25).
- Lecture 13: Hopf theorem on ergodicity of geodesic flow (October 27).
- Lecture 14: Mixing, weak mixing, ergodicity (November 1).
- Lecture 15: Weak mixing: spectral characterization (November 3).
- Lecture 16: Spectral theorem and tensor product (November 8).
- Lecture 17: Weak mixing and spectral theorem (November 10).
- Lecture 18: Ergodic decomposition (November 17).
- Lecture 19: Disintegration and unique ergodicity (November 22).
- Lecture 20: Expanding maps (November 24).
- Lecture 21: Entropy (November 29).
- Lecture 22: Ratner theorems (December 1).

- Assignment 1: Stone-Weierstrass theorem (results) (August 23).
- Assignment 2: Radon-Nikodym theorem (results) (August 31).
- Assignment 3: Tychonoff theorem (results) (September 5).
- Assignment 4: Hahn-Banach theorem (results) (September 12).
- Assignment 5: Krein-Milman theorem (results) (September 19).
- Assignment 6: Regular measures (results) (September 26).
- Home assignment 7: Lie groups (results) (October 18).
- Home assignment 8: hyperbolic geometry (results) (October 27).
- Home assignment 9: orthogonal group (results) (November 10).
- Home assignment 10: uniquely ergodic measures (results) (November 22).
- Total score for all assignments.

- Books and articles
- Exam problems
- Personal problem sets, obtained randomly with this program.
- Final scores (to be added).

Misha VerbitskyIMPA |