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).

• 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.
• Home assignment 6: Isometries of the hyperbolic plane.

Miscellanea

• Reading list

Misha Verbitsky IMPA