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Colloquium March 8

Date: Wednesday March 8

Time: 16:00 to 17:00

Place: 455 McBryde (Commons Room)

Speaker: Chris Hruska of Univ of Chicago

Title: Nonpositively curved spaces with isolated flats

Abstract

In the 1980s Gromov popularized the study of finitely generated groups using geometric techniques. He introduced and popularized notions of negative and nonpositive curvature in group theory, which have been highly influential in shaping the field of geometric group theory over the last two decades. The theory of negatively curved groups is extremely rich and exhibits many strong stability properties. On the other hand, the theory of nonpositively curved groups is much more delicate and less understood.

In my thesis, I introduced the class of nonpositively curved groups with ``isolated flats''. These groups occur naturally throughout group theory and low-dimensional topology and can be considered as the simplest nontrivial generalization of a negatively curved group. They have many properties in common with negatively curved groups. In particular, in joint work with Bruce Kleiner, I have shown that such a group is relatively hyperbolic with respect to virtually abelian subgroups.

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