MATHEMATICS COLLOQUIUM
Speaker: Ilia Binder
Title: Conformal Geometry of Planar Domains.
Affiliation: Harvard University.
Date: Friday, October 27.
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 mappings
technique. One can establish a 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 the
non simply connected case is the same as for the
simply connected one. We establish the conjecture
for a particular class of planar domains, the basins
of attraction to infity of polynomials.
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