Slides:

- Lecture 1: Complex manifolds (January 6).
- Lecture 2: Conformal structures (January 8).
- Lecture 3: Homogeneous spaces (January 10).
- Lecture 4: Möbius group (January 13).
- Lecture 5: basic notions about the Lie groups (January 15).
- Lecture 6: Möbius group (2) (January 17).
- Lecture 7: Poincaré plane (January 22).
- Lecture 8: Geodesics on Poincaré plane (February 03).
- Lecture 8 1/2: Geodesics on Poincaré plane and polygonal tilings (February 05).
- Lecture 9: Kobayashi pseudometric and Arzela-Ascoli theorem (January 24).
- Lecture 10: Riemann mapping theorem (January 27).
- Lecture 11: Fatou and Julia sets (January 31).
- Lecture 12: Ramified coverings (February 10).
- Lecture 13: Tilings and polyhedral hyperbolic manifolds (February 12).
- Lecture 14: Flow of diffeomorphisms (February 14).
- Lecture 15: Frobenius theorem (February 17).
- Lecture 16: Local systems (February 19).
- Lecture 17: Riemann-Hilbert correspondence (February 21).
- Lecture 18: Flat affine manifolds and Newlander-Nirenberg theorem (February 28)

- Home assignment 1: Lie groups
- Home assignment 2: Fundamental group and covering maps
- Home assignment 3: Pointwise and uniform convergence
- Home assignment 4: Tensor product
- Home assignment 5: Hyperbolic isometries

Other materials

- Reading list
- Class test 1 (January 29). Results.
- Class test 2 (February 7). Results.
- Exam problems
- Personal problem sets, obtained randomly with this program.
- Results of exam and final grade.

Misha VerbitskyIMPA |