Coarse differentiation and large scale geometry of solvable groups
Mini-course for graduate students
July 28 - August 8, 2008
In the early 80's Gromov initiated a program to study finitely generated groups up to quasi-isometry. This program was motivated by rigidity properties of lattices in Lie groups. A lattice Γ in a group G is a discrete subgroup where the quotient G/Γ has finite volume. Gromov's own major theorem in this direction is a rigidity result for lattices in nilpotent Lie groups.
In the 1990's, a series of dramatic results led to the completion of the Gromov program for lattices in semisimple Lie groups. The next natural class of examples to consider are lattices in solvable Lie groups, and even results for the simplest examples were elusive for a considerable time.
The main focus of this summer school will be joint work of Eskin, Fisher and Whyte in which the first results on quasi-isometry classification of lattices in solvable Lie groups were proven. The key innovation in the proofs of these results is a method of coarse differentiation, which will be discussed in detail during the school. These methods also lead to some interesting results for groups quasi-isometric to homogeneous graphs that will be discussed during the school. Further applications due to Irine Peng will also be discussed.
David Fisher, Indiana University
Kevin Whyte, University of Illinois at Chicago
Tullia Dymarz, Yale University
Irine Peng, University of Chicago
Mladen Bestvina, University of Utah
Ken Bromberg, University of Utah
Kevin Wortman, University of Utah
Anyone may apply to attend the mini-course.