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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.

DateNameTitle
Jan 14Lorenzo Ruffoni (SUNY Binghamton)[expand title=”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.[/expand]
Jan 21No Seminar[expand title=””] Abstract:
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Jan 28No Seminar [expand title=””] Abstract:
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Feb
4		Group discussion[expand title=”Open problem session”] Possible topics: asymptotic cones of groups, surface bundles over surfaces
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Feb 11Katherine Goldman (McGill University)[expand title=”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.
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Feb 18Sebastian Hurtado (Yale)[expand title=”Thin vs Lattice”] Abstract: The following elementary question seems to be open:

Suppose a group G of 2×2 matrices contains SL_2(Z), and is contained in SL_2(Z(\sqrt(2)), must G = SL_2(Z) or G = SL_2(Z[\sqrt(2)]) up to finite index?

This question fits in the general problem of understanding when a discrete subgroup in a (typically higher rank) Lie group has finite or infinite covolume. We will discuss some famous related problems, and prove some results based on the ideas of Margulis in the proof of arithmeticity and related work of Venkataramana-Chatterji.

All these notions will be explained, and the talk will be accessible (hopefully) to a large audience. Based on ongoing work with Subhadip Dey. [/expand]
Feb 25Leo Delage (Tufts)[expand title=”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.
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Mar
4		Sam Hughes (Bonn)[expand title=”On finite quotients”]Abstract: In this talk I will survey a number of recent results regarding (relative) profinite rigidity of certain groups (3-manifold groups,Coxeter groups, free-by-cyclic groups, Kaehler groups). Here profinite rigidity asks how much of information about a finitely generated residually finite group can be recovered from its finite quotients. From an algebraic geometry viewpoint this is essentially asking when the algebraic fundamental group determines an aspherical projective variety up to biholomorphism (assuming residual finiteness of the topological fundamental group). Much of the input will come from developments around the world of 3-manifold topology, building on the Virtual Fibring Theorem of Agol. With this in hand (and time permitting) I will discuss work of Wilton—Zalesskii, Wilkes, and Liu on rigidity amongst 3-manifold groups, work of myself and Kudlinska on rigidity amongst free-by-cyclic groups, and work of myself, Llosa Isenrich, Py, Stover, and Vidussi on rigidity amongst Kaehler groups.[/expand]
Mar 11Annette Karrer (Ohio State)[expand title=”Connected components in Morse boundaries of right-angled Coxeter groups”] Abstract:
Every finitely generated group G has an associated topological space, called a Morse boundary, that captures the hyperbolic-like behavior of G at infinity. It was introduced by Cordes generalizing the contracting boundary invented by Charney–Sultan. In this talk, we study subgroups arising from connected components in Morse boundaries of right-angled Coxeter groups and of such that are quasi-isometric to right-angled Coxeter groups. This talk is based on two projects. One is joint work with Bobby Miraftab and Stefanie Zbinden. The other one is joint work in progress with Matthew Cordes and Kim Ruane.[/expand]
Mar 18No SeminarSpring Break
Mar 25Leo Delage (Tufts)[expand title=”Exponential growth rates and free-by-cyclic groups (part 2)”] Abstract: This is the sequel to the talk I gave on February, 25th 2025 which was mostly about uniform exponential growth. This second part will be more focused on explicit calculations of exponential growth rates. Examples where this is completely possible are sparse but they appeal to various methods. In particular, I would like to sketch some estimates for certain free-by-cyclic groups.[/expand]
Apr
1		Barry Minemyer (Commonwealth – Bloomsburg)[expand title=”High dimensional hyperbolic Coxeter groups that virtually fiber”] Abstract: The main result to be presented is that there exist (infinitely many isomorphism classes of) hyperbolic right-angled Coxeter groups of every virtual cohomological dimension that virtually algebraically fiber over the integers.  The proof of this result combines a “combinatorial game” developed by Jankiewicz, Norin, and Wise with a generalization and improvement of a construction due to Osajda that involves a new “simplicial thickening process”.  The speaker plans to present a lot of background material as well as several examples, and so this talk should be accessible to a wide audience.  All research presented in this talk is joint work with Lafont, Sorcar, Stover, and Wells.[/expand]
Apr 8Bena Tshishiku (Brown)[expand title=”Finite group actions on 3-manifolds and Nielsen realization”] Abstract: For a manifold M, the Nielsen realization problem asks when a group of symmetries of the fundamental group π_1(M) is realized by a group of homeomorphisms of M. This problem was posed in different forms by Nielsen (1930s) and Thurston (1970s) and has connections to geometry, dynamics, and rigidity. This talk will focus on recent work and open problems related to Nielsen realization for 3-manifolds. 
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Apr 15Joshua Perlmutter (Brandeis)[expand title=”The Morse Local-to-Global Property for Graph Products”] Abstract: Morse local-to-global (MLTG) groups are a generalization of hyperbolic groups that includes CAT(0) groups, hierarchically hyperbolic groups (HHGs), and injective groups. MLTG groups have many nice properties including a regular language for Morse geodesics and a growth rate gap for stable subgroups. It is natural to ask how large the class of MLTG groups is. In this talk, I will use HHG techniques to expand the class of known MLTG groups by showing that graph products of MLTG groups are MLTG.[/expand]
Apr 22Ben Knudsen (Northeastern)[expand title=”Representation asymptotics in the homology of pure graph braid groups”] Abstract: The homology groups of the unordered configuration spaces of a graph form a finitely generated module over the polynomial ring generated by its edges; in particular, each Betti number is eventually equal to a polynomial in the number of particles, an analogue of classical homological stability. Wishing to lift this result to an analogue of representation stability, one encounters the unavoidable fact that the corresponding algebraic structure at the level of ordered configuration spaces is non-Noetherian. Thus, finite generation results are likely to be neither useful nor within easy reach. Drawing on ideas from twisted algebra and factorization homology, we circumvent this obstacle to give a complete asymptotic calculation of the Betti numbers of pure graph braid groups over any field and, in characteristic zero, of the multiplicities of irreducible representations of the symmetric groups. This talk represents joint work with Hainaut and Wawrykow, building on joint work with An and Drummond-Cole.[/expand]
Apr 30Macarena Arenas (Cambridge)** Seminar will be held on Wed. Apr. 30 at 1:30pm in JCC 140. **

[expand title=”The cubical route to understanding Artin groups”] Abstract: Artin groups simultaneously generalise braid groups, free groups, and free abelian groups. They are closely related to Coxeter groups, and like these, can be defined in terms of labelled simplicial graphs. Despite their seemingly straightforward combinatorial nature, hardly anything is known about arbitrary Artin groups, and many outstanding questions remain unanswered for large subclasses of these groups.

In this talk we will explain how to view an Artin group as a quotient of a cubulated group in a way that encodes many aspects of its geometry. We will then explain how this viewpoint – cubical small-cancellation theory – allows us to understand in many cases important properties of the group, such as asphericity and cubulability.
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