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Mathematics Colloquium


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


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