The Geometry of Hyperbolic Groups
Talk by Dr. Emily Stark (Technion - Israel Institute of Technology, Haifa, Israel)
2/13/2019 Wilson Hall 1-144 3:10-4:00pm
Hyperbolic manifolds play an important role in geometry and topology, and in the 1980s Gromov introduced a notion of large-scale negative curvature that is strong enough to capture many salient features of these manifolds, yet broad enough to apply in a more coarse setting. In this talk, I will discuss groups that have negative curvature in the sense of Gromov. Viewing finitely generated groups as geometric objects offers a powerful perspective because groups that have a similar large-scale geometry often share common algebraic structure. I will present results from my research, focusing on examples that arise naturally in low-dimensional topology, including surface amalgams and free-by-cyclic groups.