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, Kim Ruane, Lorenzo Ruffoni and Genevieve Walsh.
Date | Name | Title | ||
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Jan 30 | Sam Hughes (University of Oxford) | BNSR invariants and ell^2 homology Abstract: Based on joint work with Dawid Kielak. In this talk I will give an overview of two families of invariants of a group: the BNSR invariants encode geometrically information about fibrings of G over the integers Z; \ell^2 homology on the other hand is an equivariant homology that accounts for all unitary representations of the group. A classical result of Wolfgang L\”uck shows that non-vanishing of \ell^2 homology obstructs the existence of mapping tori structures, here we will generalise this result to the BNSR invariants and discuss some of the difficulties that arise. | ||
Feb 20 | Jacob Garcia (UC Riverside/Smith College) | Characterizations of Stability via Morse Limit Sets Abstract: An important example of Kleinian groups are the convex cocompact groups: every infinite order element of these groups is a loxodromic, and these groups are exactly the ones which admit Kleinian manifolds. A well known fact of convex cocompact groups is that they can be characterized exactly as the groups whose limit sets, on the visual boundary, are completely conical, or equivalently, completely horospherical. Convex cocompactness has been studied in the context of many non-hyperbolic spaces, such as mapping class groups, and has recently been generalized to the notion of subgroup stability. By using an analog of the visual boundary called the Morse boundary, a quasi-isometry invariant which “sees” hyperbolic directions for non-hyperbolic spaces, we show that subgroup stability is exactly classified by limit set conditions on the Morse Boundary which are analogous to the limit set conditions from the convex cocompact setting. | ||
Feb 27 | Tam Cheetham-West (Yale University) | Finite quotients of four-punctured sphere bundle groups Abstract: The finite quotients of the fundamental group of a 3-manifold are the deck groups of its finite regular covers. We often pass to these finite-sheeted covers for different reasons, and these deck groups are organized into a topological group called the profinite completion of a 3-manifold group. In this talk, we will discuss how to leverage certain properties of the mapping class group of the four-punctured sphere to study the profinite completions of the fundamental groups of fibered hyperbolic four-punctured sphere bundles over the circle. | ||
Mar 12 | Andrea Tamburelli (University of Pisa) | Length spectrum compactification of the SL(3,R)-Hitchin component Abstract: Higher Teichmuller theory studies geometric and dynamical properties of surface groups representations into higher rank Lie groups. One of these higher Teichmuller spaces is the SL(3,R)-Hitchin component, a connected component in the SL(3,R)-character variety that entirely consists of faithful and discrete representations that are the holonomies of convex real projective structures on a surface. In a joint work with Charles Ouyang, inspired by Bonahon’s interpretation of Thurston’s compactification of Teichmuller space by means of geodesic currents, we describe the length spectrum compactification of the SL(3,R)-Hitchin component. We interpret the boundary points as hybrid geometric structures on a surface that are in part flat and in part laminar. If time permits, we will give another interpretation of our main result in terms of harmonic maps to SL(3,R)/SO(3) and Euclidean buildings. | ||
Mar 26 | Jill Mastrocola (Brandeis University) | TBA Abstract: TBA | ||
Apr 2 | Merlin Incerti-Medici (Vienna) | TBA Abstract: TBA | ||
Apr 9 | Kevin Schreve (Louisiana State University) | TBA Abstract: TBA | ||
Apr 16 | Bena Tshishiku (Brown University) | TBA Abstract: TBA | ||
Apr 23 | Dave Constantine (Wesleyan University) | TBA Abstract: TBA |