Our seminar meets Tuesdays at 4:30 in JCC 502. Talks are in person and also streamed on Zoom. You can subscribe to the GGTT mailing list at https://elist.tufts.edu/sympa/info/ggtt for details and announcements. The seminar organizers are Corey Bregman, Nima Hoda, Kim Ruane and Genevieve Walsh.
| Date | Name | Title | ||
|---|---|---|---|---|
| Jan 14 | Lorenzo Ruffoni (SUNY Binghamton) | Atoroidal surface bundles with signature zero Abstract: Hyperbolic geometry has been a powerful tool in the study of manifold topology. Beyond the classical theory of surfaces, Thurston showed that the family of surface bundles over the circle is a rich source of hyperbolic 3-manifolds. In dimension 4, the correct analogue is given surface bundles over surfaces. In order for such a bundle to admit a hyperbolic metric, it needs to satisfy some conditions, such as being atoroidal and having signature zero. Surprisingly enough, the first examples of atoroidal surface bundles over surfaces were constructed only recently by Kent-Leininger. In this talk I’ll explain why these examples also have signature zero, meaning that they could admit hyperbolic metrics. This is joint work with J-F. Lafont and N. Miller. | ||
| Jan 21 | No Seminar | Abstract: | ||
| Jan 28 | TBA | Abstract: | ||
| Feb 4 | Group discussion | Open problem session Possible topics: asymptotic cones of groups, surface bundles over surfaces | ||
| Feb 11 | Katherine Goldman (McGill University) | Residual properties of 2-dimensional Artin groups It is a longstanding open question to determine which Artin groups are residually finite. Past results have followed from linearity (e.g., for spherical-type or virtually cocompact special Artin groups) or product decompositions in rank 3. We present a new approach to this problem using intermediate quotients to so-called Shephard groups. These Shephard groups possess their own interesting (and sometimes counterintuitive) geometry which we can leverage to give new information about their corresponding Artin groups in some cases. As a highlight of this connection, we show that an Artin group which is simultaneously 2-dimensional, hyperbolic-type, and FC-type is residually finite. One of the key features of the proof we will discuss is the fact that hyperbolic-type 2-dimensional Shephard groups are relatively hyperbolic, which is almost never true of Artin groups. | ||
| Feb 18 | Sebastian Hurtado (Yale) | TBA | ||
| Feb 25 | Leo Delage (Tufts) | Exponential growth rates and free-by-cyclic groups Abstract: The growth rates of exponentially-growing groups have attracted attention since the observation by Koubi that hyperbolic groups have uniform exponential growth. Recent developments on the “growth spectrum” (i.e. the set of exponential growth rates of a same finitely generated group obtained from its different generating systems) have followed the progress of equation theory in groups. In particular, hyperbolic groups and certain acylindrically hyperbolic groups (including free-by-cyclic groups) have well-ordered growth spectrum. However, apart from a few cases (e.g. free groups), little is known about the minimizing set of generators. In fact, examples of explicit growth rate calculations are still very sparse. After surveying these topics, I will detail some estimates for growth rates of free-by-cyclic groups. | ||
| Mar 4 | Sam Hughes (Bonn) | TBA | ||
| Mar 11 | Annette Karrer (Ohio State) | TBA Abstract: | ||
| Mar 18 | No Seminar | Spring Break | ||
| Mar 25 | Merlin Incerti-Medici (Wien) | Abstract: | ||
| Apr 1 | Barry Minemyer | TBA Abstract: | ||
| Apr 8 | Bena Tshishiku (Brown) | Abstract: | ||
| Apr 15 | TBA | Abstract: | ||
| Apr 22 | TBA | Abstract: |