Mathematics Colloquium
Speaker: Ilia Binder
Title: Conformal Geometry of Planar Domains.
Affiliation: Harvard University.
Date: Friday, April 28.
Place and Time: Room 101 - Love Building, 3:35-4:35 pm.
Refreshments: Room 204 - Love Building, 3:00 pm.
Abstract. We study the conformal, harmonic and metric geometry
of planar domains. To be more precise, we investigate sharp metrical
bounds for the rotation of Green lines and the relation to the properties
of harmonic measure - so called universal spectra.
The theory is well established for simply connected domains, since
one can use the conformal mapping technique. One can establish nice
connection between the geometric properties of the boundaries of the
simply connected domains and the distortion properties of their
Riemann maps.
The conjecture is that the universal spectra for non simply connected
case are the same as for simply connected one. We establish the
conjecture for a particular class of planar domains, the basins
of attraction to infinity of polynomials.
|