Title: Braids, trees, and operads

Author: Jack Morava

AMS classification: 55R810, 14N35, 20F36

Address: The Johns Hopkins University
Baltimore 21218 Maryland

e-mail: jack@math.jhu.edu

Abstract: The space of unordered configurations of distinct points
in the plane is aspherical, with Artin's braid group as its fundamental 
group. Remarkably enough, the space of ordered configurations of 
distinct points on the real projective line, modulo projective equivalence,
has a natural compactification (as a space of equivalence classes of trees)
which is also (by a theorem of Davis, Januszkiewicz, and Scott) aspherical.
The classical braid groups are ubiquitous in modern mathematics, with 
applications from the theory of operads to the study of the Galois group
of the rationals. The fundamental groups of these new configuration 
spaces are not braid groups, but they have many similar formal properties.
This talk [at the Gdansk conference on algebraic topology 05-06-01] is an 
introduction to their study.