Coarse geometry of solvable groups

David Fisher

Indiana University

Brandeis University

Thursday, February 5, 2009

Talk at 4:30 p.m. in 317 Goldsmith Hall

Tea at 4:00 p.m. in 300 Goldsmith Hall

Abstract: 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 $\Gamma$ in a group $G$ is a discrete subgroup where the quotient $G/\Gamma$ 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. In around 2005, Eskin, Whyte and I introduced a technique of coarse differentiation that led to the first quasi-isometric rigidity results for lattices in solvable Lie groups. I will describe something about these results and techniques and will also talk about what is involved in extending the results to more general solvable Lie groups. Some of this is work of Irine Peng and some is joint work with Eskin and Peng.

I will also describe some interesting results concerning groups quasi-isometric to homogeneous graphs that follow from the same methods.

Home Web page: Alexandru I. Suciu Posted: January 23, 2009
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