The Geometry of Outer Space:
Investigated through its analogy with Teichmueller space
June 24, 2013 - July 21, 2013
There is a long history of utilizing the geometry of an object to better understand the group of isometries acting on it, a classical example being Lie groups acting on homogeneous spaces.
More recently Thurston and his followers used the geometry of Teichmueller space to aid in understanding the mapping class groups of surfaces.
While the situation is richly more complicated, evidence has indicated that much of the behavior of a mapping class group acting on its Teichmueller space is mirrored in the behavior of the outer automorphism group of a free group acting on its respective Outer space.
This analogy has inspired exploration into the geometry of Outer space. However, progress has been markedly slow.
With several recent break-throughs, the perfect setting exists for a group of mathematicians with the necessary collective knowledge-base, adequate time, and a common location, to make awaited significant progress in finally understanding the geometry of Outer space.
The purpose of our program is to facillitate precisely this.
This program is funded by:
NSF Grant DMS - 1331129,
Labex Archimède Research in Residence Grant,
This program is organized by: Thierry Coulbois, Arnaud Hilion, and Catherine Pfaff