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:
- Donald E. Marshall and John B. Garnett, Harmonic measure, Cambridge University Press, 2005
- Christian Pommerenke, Boundary Behaviour of Conformal Maps, Springer, 1992
Course notes:
- Conformal maps: Distortion Theory.
- Caratheodory convergence.
- Extremal length method.
- Boundary behavior of conformal maps: Wolff Lemma and Lavrentiev estimate.
- Prime ends.
- Loewner Evolution.
- Chordal Loewner Evolution.
- Martingales.
- Bloch martingales and conformal maps.
- Dirichlet problem and harmonic measure.
- On Hasdorff dimension.
- Proof of Makarov's dimension Theorem: the upper bound.
- Proof of Makarov's dimension Theorem: the lower bound.
- Brownian Motion: some elementary properties.
- Ito calculus.