We'll read and discuss various papers related to these topics. As this is a Berstein seminar, most classes will consist of student lectures, and the content will be chosen collectively by the participants. I'll try to point out open questions and possible research directions as they arise.

- [G] M. Gromov, Hyperbolic groups, in Essays in Group Theory, edited by Gersten.
- [BH] M. Bridson and A. Haefliger, Metric spaces of nonpositive curvature, especially chapters III.H and III.Γ.
- [CDP] M. Coornaert, T. Delzant and A. Papadopoulos, Géométrie et théorie des groupes.
- More to come...

Date |
Speaker |
Topic |

1/25/17 | Jason | Intro to hyperbolicity |

1/27/17 | Jason | Central problems in hyperbolic groups |

1/30/17 - 2/1/17 | Teddy | Quasi-geodesic stability [BH, III.H.1] |

2/3/17 | Oliver | Isometries of hyperbolic spaces [CDP, Ch. 9] |

2/6/17 - 2/8/17 | Tim | Baumslag-Solitar subgroups (see here) |

2/10/17 | Florian | Rips complex of a hyperbolic group [BH, III.Γ.3] |

2/13/17 | Carolyn Abbott (special guest!) | Acylindrically hyperbolic groups |

2/15/17 | Yu-chan | Linear isoperimetric function. See Notes On Hyperbolic and Automatic Groups, by Patty & Papasoglu, Section 3.4 (cf. [BH, III.H.2]) |

2/17/17 | Jason | CAT(0) geometry and hyperbolicity |

2/22/17 - 2/24/17 | Drew | Random groups. See: Sharp phase transition theorems for hyperbolicity of random groups, by Yann Ollivier. |

2/27/17 | Pallavi | Rips construction. See: Incoherent negatively curved groups, by Daniel Wise. |

3/1/17 | Teddy | CAT(0) spaces with isolated flats. See Geometric invariants of spaces with isolated flats by Hruska, and Hadamard spaces with isolated flats by Hruska and Kleiner. |

3/3/17 | Jason | Cone types and automata. [BH, III.Γ.2] |

3/6/17 | Teddy | CAT(0) spaces with isolated flats, continued. |

3/8/17 - 3/10/17 | Oliver | Boundaries of hyperbolic groups. Reference M. Bestvina and G. Mess, The boundary of negatively curved groups. |

3/13/17 | Drew | Surface subgroups of random groups. Reference: D. Calegari and A. Walker Random groups contain surface subgroups. |

3/20/17 - 3/22/17 | Yu-chan | Cannon's conjecture and the surface subgroup problem. Reference: V. Markovic, Criterion for Cannon's conjecture. |

Jason | Some aspects of Agol's theorem | |

3/29/17 | Corey Bregman | Gromov norm and bounded cohomology |

4/10/17 | Oliver | Relatively hyperbolic groups |

4/12/17 | Pallavi | Classifying one-dimensional boundaries of hyperbolic groups. Reference: M. Kapovich and B. Kleiner, Hyperbolic groups with low-dimensional boundary. |

4/14/17-4/17/17 | Teddy | Bestvina-Feighn combination theorem. Reference: M. Bestvina and M. Feighn, A combination theorem for negatively curved groups. |

4/21/17 | Drew | More on Markovic's paper Criterion for Cannon's conjecture. |

4/24/17 | James Farre | Mineyev's theorem on boundedness of cohomology for hyperbolic groups. Reference: I. Mineyev, Straightening and bounded cohomology of hyperbolic groups. |

Last Updated 2017-04-21