May 8 - 12, 2006

University of Michigan
Ann Arbor, Michigan

Registration

Lodging

Participants

Maps/Directions
Ann Arbor Information
University of Michigan
Mathematics Department

Organizers
Mario Bonk
Juha Heinonen

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Modern Developments in Geometric Function Theory:
Workshop for Graduate Students and Postdocs

SPEAKERS

• Mario Bonk - Quasiconformal geometry of fractals
• Alexandre Eremenko - Geometric Theory of Meromorphic Functions
• Juha Heinonen - Quasiconformal mappings and bi-Lipschitz mappings
• Tadeusz Iwaniec - The energy integrals -- an invitation to harmonic analysis and nonlinear PDEs
• Steffen Rohde - SLE and random (quasi-)conformal maps

SCHEDULE

In addition, there will be daily open discussion/problem session 4:30 - 6:00 pm in 1324 East Hall Psychology Auditorium.

PRELIMINARIES

Dear Participant,

We are listing here some topics that you could review before the May workshop. This may help you to follow the lectures.

Prerequisites: We assume that everyone is familiar with basic graduate real and complex analysis as well as basic concepts of probability. In particular, we assume basic knowledge of the following topics and objects:

- Uniformization theorem for Riemann surfaces
- Subharmonic functions - Riemannian metric
- Sobolev space
- Basic properties of standard linear function spaces (e.g. weak convergence)
- Independence of random variables
- Borel-Cantelli lemma

Moreover, the following concepts will be quickly reviewed but prior knowledge would be most helpful:

-Modulus of a curve family
- Quasisymmetric mappings between metric spaces (as in Chapters 7 and 10-11 of the book "Lectures in Analysis on Metric Spaces" by J. Heinonen).

Familiarity of Brownian motion, and the Beltrami equation in connection with quasiconformal mappings would also be helpful. (For the latter, see e.g. "Lectures on quasiconformal mappings" by L. Ahlfors.)

The Organizers

Contact:

Mario Bonk (mbonk@umich.edu)
Juha Heinonen (juha@umich.edu)