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.
Extra class Monday, November 25, 10-11am, BA6180. The last class will be on Wednesday, November 27.

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.
  10. Dirichlet problem and harmonic measure.
  11. On Hasdorff dimension.
  12. Proof of Makarov's dimension Theorem: the upper bound.
  13. Proof of Makarov's dimension Theorem: the lower bound.
  14. Brownian Motion: some elementary properties.
  15. Ito calculus.