Geometric function theory

Fall 2019


Web page: http://www.math.toronto.edu/ilia/MAT1007.2019/.

Class Location & Time: Mon, 11:00 AM - 12:00 PM and Wed, 10:00 AM - 12:00 PM; BA6180
Extra classes: September 30, October 7, October 21: 10:00-11:00am; BA6180
No class October 28. Guest lecture by Adi Glucksam on October 30.

Instructor: Ilia Binder (ilia@math.toronto.edu), BA6118.

Textbooks:

  1. Donald E. Marshall and John B. Garnett, Harmonic measure, Cambridge University Press, 2005
  2. Christian Pommerenke, Boundary Behaviour of Conformal Maps, Springer, 1992

Course notes:

  1. Conformal maps: Distortion Theory.
  2. Caratheodory convergence.
  3. Extremal length method.
  4. Boundary behavior of conformal maps: Wolff Lemma and Lavrentiev estimate.
  5. Prime ends.
  6. Loewner Evolution.
  7. Chordal Loewner Evolution.
  8. Martingales.
  9. Bloch martingales and conformal maps.