## Spring 2019

Seminar meets Tuesdays at 4:30 in BP 101 in the Tufts Math Department. You can subscribe to the GGTT mailing list here. The seminar organizers are Robert Kropholler, Kim Ruane and Genevieve Walsh.

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Date |
Name |
Title |
---|---|---|

Jan 22 | Genevieve Walsh | Relatively hyperbolic groups with planar boundary
Abstract: I will describe what a relatively hyperbolic group is, and give a lot of examples where the boundary is planar. Furthermore, I will explore some of the interesting phenomena that can occur and explain the significance of cut points in the boundary. Lastly I will discuss restrictions on the peripheral groups when the boundary is planar and without cut points.This is joint work in progress with Chris Hruska |

Jan 29 | Bena Tshishiku | Surface bundles, monodromy, and arithmetic groups
Abstract: Fiber bundles with fiber a surface arise in many areas including hyperbolic geometry, symplectic geometry, and algebraic geometry. Up to isomorphism, a surface bundle is completely determined by its monodromy representation, which is a homomorphism to a mapping class group. This allows one to use algebra to study the topology of surface bundles. Unfortunately, the monodromy representation is typically difficult to “compute” (e.g. determine its image). In this talk, I will discuss some recent work toward computing monodromy groups for holomorphic surface bundles, including certain examples of Atiyah and Kodaira. This can be applied to the problem of counting the number of ways that certain 4-manifolds fiber over a surface. This is joint work with Nick Salter. |

Feb 5 | Kim Ruane | An Introduction to Semistability at Infinity for Groups |

Feb 12 | Michael Ben-Zvi | Informal Talk |

Feb 19 | Thomas Ng | Virtually torsion-free CAT(0) cubical IFP groups have uniform exponential growth
Abstract: A group is said to have uniform exponential growth if the number of elements that can be spelled with words of bounded length is bounded below by a single exponential function over all generating sets. In 1981, Gromov asked whether all groups with exponential growing group in fact have uniform exponential growth. While this was shown not to be the case in general, it has been answered affirmatively for many natural classes of groups such as hyperbolic groups, linear groups, and the mapping class groups of a surface. In 2018, Kar-Sageev show that groups acting properly on 2-dimensional CAT(0) cube complexes by loxodromic isometries either have uniform exponential growth or are virtually abelian by explicitly exhibiting free semigroups whose generators have uniformly bounded word length whenever they exist. These free semigroups witness the uniform exponential growth of the group. I will explain how certain arrangements of hyperplane orbits can be used to build loxodromic isometries generating free semigroups and then describe how to use the convex hull of their axes and the Bowditch boundary to extend Kar and Sageev’s result to CAT(0) cube complexes with isolated flats.
This is joint work with Radhika Gupta and Kasia Jankiewicz. |

Feb 26 | Davide Spriano | TBA
Abstract: TBA |

Mar 5 | Rylee Lyman | Polynomially-growing Palindromic Automorphisms of Free Groups and CAT(0) Free-by-cyclic Groups
Abstract: Corresponding to each automorphism of a free group, there is a cyclic semi-direct extension of the free group. Gersten in 1994 gave an example of such a free-by-cyclic group which is a “poison subgroup” for non-positive curvatureâ€”any group containing it cannot act geometrically on a CAT(0) space. His argument is both beautiful and geometric. Gersten’s proof provides context for our result; we show that in contrast with the general case, many free-by-cyclic groups associated to polynomially-growing palindromic automorphisms do admit a geometric action on a CAT(0) space. |

Mar 12 | Federico Vigolo | TBA
Abstract: TBA |

Mar 19 | No Seminar | No Seminar |

Mar 26 | No Seminar | No Seminar |

Apr 2 | No Seminar | No Seminar |

Apr 9 | TBA | TBA
Abstract:TBA |

Apr 16 | TBA | TBA
Abstract: TBA |

Apr 23 | Behrang Forghani | TBA
Abstract:TBA |

Apr 30 | Tim Susse | TBA
Abstract:TBA |