Misha Verbitsky

Instituto Nacional de Matemática Pura e Aplicada

Complex variables

Sala 232, Mondays, Wednesdays, Fridays, 17:00-19:00, January-February 2020

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 Verbitsky IMPA