MAT 626, Topics in complex analysis: geomtric function theory, Fall 1999

Christopher Bishop

Professor, Mathematics
SUNY Stony Brook

Office: 4-112 Mathematics Building
Phone: (516)-632-8289
Dept. Phone: (516)-632-8290
FAX: (516)-632-7631

Send me email at: bishop@math.sunysb.edu

NEW Time and place: MF 10:10-11:30 , room P-131, Math Tower

Geometric function theory covers many topics, but is primarily concerned with 1-1 analytic funtions of one complex variable (i.e., univalent functions). There has been a lot of activity in the area during the 80's and 90's and in this course we will try to cover some of these recent developments, while somehow fitting in the classcal backgroun that we need.

We will follow a soon to be published text by John Garnett (UCLA) and Don Marshall (UW, Seattle). The main focus will be on Chapters 4,5,6. I will provide photocopies of the text at the beginning of the course. You can look at the table of contents by clicking on these links for a dvi file , or postscript file

Some of the topics we will discuss in detail include: Riemann mapping theorem, Koebe 1/4 theorem, harmonic measure, extremal length, Hardy spaces, BMO, quasiconformal mappings, chord-arc curves, A-infinity measures, Hausdorff dimension, the Hayman-Wu theorem, Makarov's theorem, the Brennan conjecture, the area function, Jones' traveling salesman theorem, Schwarzian derivatives, Bishop-Jones L^2 theory for Schwarzians, generalized Hayman-Wu problem.