The Geometric Function Theory Seminar -- Fall 2007

Wednesdays 3:10-4:00 -- East Hall 4096

To schedule a talk, or for more information, please contact Daniel Meyer (danimey 'at' umich.edu).

Wednesday, September 26.

Speaker: Jasun Gong (UM) .
Title: Derivations and Currents on Metric Spaces

Abstract: In this talk we will examine the role of N. Weaver's theory
of derivations in the subject of analysis on metric spaces. In
particular, we will relate this theory to that of currents on metric
spaces, as introduced by L. Ambrosio and B. Kirchheim. We will also
discuss some results in the cases of the line R^1 and the plane R^2.

Wednesday, September 19.

Speaker: Roger W. Barnard (Texas Tech).
Title: How far can you deform a disk under a convex map?

Abstract: In this talk we discuss how we apply variational techniques and special function theory to verify some conjectures of C. Pommerenke's and of D. Minda on the sharp upper bound for the Schwarzian derivative of hyperbolic convex maps. This completes the classification of the extremal domains for the Schwarzian in all three classical geometries hence answering the question first posed in the 50's as to how far one can distort a disk under a convex map in Euclidean, spherical and hyperbolic geometries.

Wednesday, September 12.

Speaker: Mario Bonk (UM).
Title: Quasiconformal flows.

Abstract: A vector field generates a quasiconformal flow if its so-called strain tenson is essentially bounded. I will give a survey on this subject and discuss some related open problems.