Groups as geometric objects

Geometry Topology Seminar Pre-talk
Monday, October 21, 2019 - 12:45pm for 1 hour (actually 50 minutes)
Skiles 006
Jacob Russell – CUNY Graduate Center – jrussellmadonia@gradcenter.cuny.edu
Justin Lanier

Gromov revolutionized the study of finitely generated groups by showing that an intrinsic metric on a group is intimately connected with the algebra of the group. This point of view has produced deep applications not only in group theory, but also topology, geometry, logic, and dynamical systems. We will start at the beginning of this story with the definitions of these metrics on groups and how notions from classical geometry can be generalized to this context.  The focus will be on how the "hyperbolic groups" exhibit geometric and dynamical feature reminiscent of the hyperbolic plane and its isometries.