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.

DateNameTitle
Jan 30Sam 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 20Jacob 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 27Tam 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 12Andrea 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 26Jill Mastrocola (Brandeis University)Locally Reducible Artin Groups and Acylindrical Hyperbolicity
Abstract:  Artin groups are a large and interesting class of groups with strong ties to Coxeter groups and mapping class groups. There are many long-standing open questions about Artin groups, and non-positively curved geometry has been a useful tool in many of the partial answers that we have. I introduce the 2-complete Artin complex for locally reducible Artin groups and discuss a combinatorial version of non-positive curvature that it satisfies, known as systolicity. I use this to show that many proper parabolic subgroups of a locally reducible Artin group are weakly malnormal, and conclude that a new class of Artin groups is acylindrically hyperbolic.
Apr 2Inanc Baykur (UMass Amherst)Geography of surface bundles over surfaces
Abstract:  An outstanding problem for surface bundles over surfaces is determining which fiber and base genera are examples with positive signatures. I will describe our recent progress (with M. Korkmaz), which resolves the problem for all but 19 cases, and explain how some open cases relate to major questions in symplectic geometry.
Apr 4
(Thu
JCC 614)
Merlin Incerti-Medici (Vienna)Automorphism groups of cocompact CAT(0) cube complexes
Abstract:  Given a cocompact CAT(0) cube complex, we study the group of its cubical isometries, which frequently forms a non-discrete tdlc group. We present a method to study these groups that is focused on our ability to understand the stabilizer subgroups. We demonstrate the potency of this method by introducing a finite, topologically generating set and discuss an important simple subgroup. If there is time, we discuss some open questions regarding the placement of these groups among non-discrete tdlc groups.
Apr 9Kevin Schreve (Louisiana State University)Orders and Fibering
Abstract: Kielak gave a fibering criterion for RFRS groups in terms of vanishing of the first L^2-Betti number. I’ll talk about an alternative, and hopefully simpler, proof of this. Joint with Boris Okun.
Apr 16Bena Tshishiku (Brown University)Mapping class group actions on 3-manifolds
Abstract: For a surface S, Thurston asked if the mapping class group Mod(S) admits a natural action on S by homeomorphisms. This relates to the existence of flat connections on S-bundles. Markovic showed no such action exists. On the other hand, miraculously(!), there is a natural action of Mod(S) on the unit tangent bundle of S. This leads one to ask if Mod(S) acts naturally on any other 3-manifolds. We discuss some partial progress toward an answer. This is joint with Lei Chen and Alina al Beaini. 
Apr 23Dave Constantine (Wesleyan University)Geodesic flow on CAT(-1) and (some) CAT(0) spaces
Abstract: How¬†do we define geodesic flow on a metric space? Which of the nice dynamical properties of geodesic flow on negatively or nonpositively¬†curved Riemannian manifolds can we prove for their metric space analogues: CAT(-1) and CAT(0) spaces? In this talk I’ll discuss some results on the geodesic flow for CAT(-1) spaces obtained jointly with Jean-Francois Lafont and Dan Thompson. Then I will report on some recent work with Ben Call, Alena Erchenko, Noelle Sawyer, and Grace Work on geodesic flow for flat surfaces with large-angle cone point singularities. These spaces include translation surfaces, and provide a first step in the direction of extending our results to the CAT(0) setting.