Seminar meets Tuesdays at 4:30 EST via Zoom. You can subscribe to the GGTT mailing list here. The Zoom link will be sent via this mailing list. This semester, the seminar organizers are Kim Ruane and Genevieve Walsh.
|Sept 22||Corey Bregman||Minimal volume entropy of free-by-cyclic groups and 2D RAAGs
Abstract: Minimal volume entropy is a Riemannian manifold invariant introduced by Gromov to study the asymptotic geometry of the universal cover, and is related to the growth of the fundamental group. Here we study an extension of this invariant to a simplicial complex X equipped with a piecewise Riemannian metric. When X is 2-dimensional and aspherical, we characterize when the minimal volume entropy vanishes in terms of an algebraic condition on the fundamental group. We apply these results to the cases of free-by-cyclic groups and 2-dimensional right-angled Artin groups, obtaining a uniform lower bound in the nonvanishing case. This is joint work with Matt Clay.
|Sept 29||Indira Chatterji||Proper actions on Lp spaces
Abstract: A group is said to have property (T) if any action on a Hilbert space, has a fixed point. I will discuss what happens to this notion when one replaces Hilbert space with a more general Lp space, and discuss in particular the case of (relatively) hyperbolic groups.
|Oct 6||Emily Stark||Deep homology and obstructing group actions
Abstract: Studying the topology of a space “at infinity” offers a powerful perspective in geometric group theory. To capture the structure at infinity relative to a subspace, one can consider relative ends and associated deep homology groups. A goal is then to compute these homology groups and use homological arguments to study these pairs of spaces. In this talk, I will explain how both goals are possible in the setting of coarse embeddings into coarse PD(n) spaces. As applications, we use homological arguments to prove that certain groups cannot act properly on a given manifold. This is joint work with Chris Hruska and Hung Cong Tran.
|Oct 13||James Farre||An application of the Milnor—Wood Inequality
Abstract: [Circle bundles over a surface have an “Euler number,” which is the
obstruction to finding a continuous section of the bundle. For flat circle
bundles, the Euler number is bounded; this is known as the Milnor—Wood
inequality. I will define flat circle bundles and the Euler number of a
bundle. Using the Milnor—Wood inequality, we will give a short and clever
proof, due to Bestvina—Church—Souto, that the point pushing subgroup of the
mapping class group of a closed surface with one marked point cannot be
realized as a group of diffeomorphisms fixing the marked point.
|Oct 20||Michelle Chu||Virtual torsion in the homology of 3-manifolds
Abstract: Hongbin Sun showed that a closed hyperbolic 3-manifold virtually contains any prescribed torsion subgroup as a direct factor in homology. In this talk we will discuss joint work with Daniel Groves generalizing Sun’s result to irreducible 3-manifolds which are not graph-manifolds.
|Oct 27||Stefano Vidussi||Algebraic fibrations of surface-by-surface groups and Kahler groups.
Abstract: I will discuss some results and questions about the behavior, with respect to algebraic fibrations, for the classes of groups above, using as reference point the fundamental groups of Kodaira fibrations, that belong to both.
|Nov 3||Qing Liu||Maps on the Morse boundary.
The Morse boundary of a proper geodesic metric space is a quasi-isometry invariant to study hyperbolic-like behaviors in the space. A quasi-isometry between two spaces induces a homeomorphism on their Morse boundaries. This homeomorphism satisfies a variety of metric properties including bi-hölder, quasi-conformal, quasi-möbius and power quasisymmetric. In this talk, we will investigate these structures on the Morse boundary which determine the interior space up to a quasi-isometry.
|Nov 10||Bena Tshishiku||Arithmeticity of free-abelian by cyclic groups
Abstract: We discuss arithmeticity of groups G(A) = ℤ^n ⋊ ℤ, where ℤ acts on ℤ^n by powers of an irreducible, hyperbolic matrix A ∈ GL(n,ℤ). The question of when G(A) is arithmetic was studied systematically by Grunewald-Platonov, but there are basic things that we still don’t know. For example, for what values of n is there an arithmetic example? We discuss some progress toward answering this question.
|Nov 17||Robert Kropholler||Homological filling functions for almost finitely presented groups.
The Dehn function of a finitely presented group is a classical invariant to study the complexity of the word problem. One can study the homological analogue of this function, namely, the homological filling function. This function is defined on the larger class of almost finitely presented groups. However, there has not been much study of the homological filling function of almost finitely presented groups. I will define all the relevant notions and discuss joint work with Noel Brady and Ignat Soroko studying these functions.
|Nov 24||Eric Chesebro||Farey recursion and the geometry of 2-bridge links.
I will explain a complicated system of recursive polynomials which describe the hyperbolic structures on the complements of 2-bridge links. The patterns in this system of polynomials can be used to efficiently compute these geometries and lend themselves to straightforward inductive proofs.
|Dec 1||No Seminar||TBA
|Dec 8||Kasia Jankiewicz||TBA