Misha Verbitsky

Instituto Nacional de Matemática Pura e Aplicada

Complex manifolds in dimension 1

Sala 236, Mondays, Wednesdays 17:00-18:30

Slides:

• Lecture 1: Complex and conformal structures (March 18).
• Lecture 2: Space forms (March 20).
• Lecture 3: Lie groups (March 25).
• Lecture 4: Möbius group (March 25).
• Lecture 5: Pseudo-Hermitian forms (April 3)
• Lecture 6: Circles on a sphere are preserved by the Möbius group (April 3).
• Lecture 7: Isometries of the Poincaré plane (April 8).
• Lecture 8: Geodesics on the Poincaré plane (April 10).
• Lecture 9: Kobayashi pseudometric (April 15).
• Lecture 10: Arzelà-Ascoli theorem and Montel theorem (April 17).
• Lecture 11: Riemann mapping theorem (April 22).
• Lecture 12: Fatou and Julia sets (April 24).
• Lecture 13: Ramified coverings (April 29).
• Lecture 14: Tilings and polyhedral manifolds (May 6).
• Lecture 15: Anan'in Theorem (May 8).
• Lecture 16: Locally constant sheaves (May 13).
• Lecture 17: Riemann-Hilbert correspondence (May 15).
• Lecture 18: Frobenius theorem (May 20).
• Lecture 19: Connections and curvature (May 22)
• Lecture 20: Riemann-Hilbert correspondence 2: flat bundles and local systems (May 27).

• Home assignment 1: holomorphic functions (results).
• Home assignment 2: quadratic forms (results).
• Home assignment 3: Lie groups (results).
• Home assignment 4: Orientation (results).
• Home assignment 5: Uniform convergence (results).
• Home assignment 6: Isometries of the hyperbolic plane (results).
• Home assignment 7: Coverings (results).
• Home assignment 8: Foliations.
• Home assignment 9: Connections and curvature.

Miscellanea

• Reading list
• Exam problems
• Personal problem sets, obtained randomly with this program.

Misha Verbitsky IMPA