The study of abstract metric geometry was initiated in the
works of K. Menger, H. Busemann and A.D. Alexandrov and, over the
years, has impacted many areas of mathematics. More recently, the
concept of large-scale (metric) geometry due to M. Gromov has proved
to be an important tool in geometric group theory. In geometric
function theory the use of metric geometry (or invariant metrics) to
study conformal and quasi-conformal mappings was initiated by L.
Ahlfors, G. Pick and O. Teichmüller. In this talk I will briefly
discuss the ideas of Ahlfors and Pick on the use of the hyperbolic
metric in complex analysis and then discuss more recent invariant
metrics in geometric function theory. In some detail, I will discuss
the geometry of the Apollonian metric. The latter was introduced by
A. Beardon in 1998 and has since been studied by many authors.
R E F R E S H M E N T S
4:00 to 4:25 PM
Kenneth W. Anderson
Memorial Reading Room
