EVENT DETAILS AND ABSTRACT

Title: Coarse differentiation of quasi-isometries and rigidity for lattices in solvable Lie groups
Speaker: Professor David Fisher
Speaker Info: Indiana University
Brief Description:
Special Note:
Abstract:

In the early 80's Gromov initiated a program to study finitely generated groups up to quasi-isometry. This program was motivated in part by rigidity properties of lattices in Lie groups. A lattice in a group G is a discrete subgroup Gamma where the quotient G / Gamma has finite volume. A major theorem of Gromov's 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. I will discuss joint work with Eskin and Whyte in which we prove the first results on quasi-isometry classification of lattices in non-nilpotent, solvable Lie groups. In particular, we prove that any group quasi-isometric to the three dimensional solvable group Sol is virtually a lattice in Sol.

The results are proven by a method of coarse differentiation, which I will outline.