|Date: Tuesday, March 19, 2013
Title: Quasi-isometric rigidity of polycyclic groups
Abstract: In his 1983 ICM address, Gromov proposed a program to classify finitely generated groups up to quasi-isometry. This program is a central part of geometric group theory. A major part of the program consists of showing that various classes of groups are quasi-isometrically rigid, i.e. that any group quasi-isometric to a group in the class is also in the class.
Eskin, Whyte and I conjecture that the class of polycyclic groups is quasi-isometrically rigid and proved quasi-isometric rigidity of the three dimensional polycyclic groups. A key ingredient is a new technique which we call coarse differentiation. This technique allows us to define a kind of derivative of a quasi-isometry despite the fact that quasi-isometries need not even be continuous.
I will discuss current progress towards proving our conjecture. Parts of this are joint with Eskin, Peng and Whyte.
Speaker: David Fisher
Institution: Indiana University