Fall 2018
Seminar meets Tuesdays at 4:30 in BP 101 in the Tufts Math Department. You can subscribe to the GGTT mailing list here. In Fall 2018, the seminar organizers are Robert Kropholler, Kim Ruane and Genevieve Walsh.
Date  Name  Title 

Sep 11  Oliver Wang  Cohomology of relatively hyperbolic groups
Abstract: Bestvina and Mess have shown that the group cohomology of a hyperbolic group is isomorphic to the Cech cohomology of the group’s boundary. To achieve this, they show that both cohomology groups are isomorphic to the compactly supported cohomology of the Rips complex. I will discuss recent work with Jason Manning, in which the cohomology of a relatively hyperbolic group pair is shown to be isomorphic to the Cech cohomology of the Bowditch boundary. If there is time, I will also discuss some corollaries. 
Sep 18  Peter Kropholler  Amenability and rank conditions on group rings
Abstract: We’ll explain how Bartholdi and Kielak’s work on cellular automata can be used to show that the integral group ring of a group satisfies the strong rank condition if and only if is amenable. This in turn can be used to prove a conjecture of Wolfgang Lueck on dimension flatness for cohomology. In addition, the results imply that the group ring can be Noetherian only if the group is amenable with max on subgroups. At present the only known such groups are polycyclic by finite. 
Sep 25  Siddhi Krishna  Taut Foliations, Positive 3Braids, and the LSpace Conjecture
Abstract: The LSpace Conjecture is taking the lowdimensional topology community by storm. It aims to relate seemingly distinct Floer homological, algebraic, and geometric properties of a closed 3manifold . In particular, it predicts a 3manifold isn’t “simple” from the perspective of HeegaardFloer homology if and only if admits a taut foliation. The reverse implication was proved by Ozsvath and Szabo. In this talk, we’ll present a new theorem supporting the forward implication. Namely, we’ll discuss how to build taut foliations for manifolds obtained by surgery on positive 3braid closures. No background in HeegaardFloer or foliation theories will be assumed. 
Oct 2  James Farre  Infinite volume and bounded cohomology
Abstract: To a hyperbolic 3manifold M, we associate the class in cohomology that computes the volume of geodesic tetrahedra in M. We will be interested in the setting that M has infinite volume, so this cohomology class is necessarily zero. To circumvent this shortcoming, we introduce bounded cohomology. As we vary the hyperbolic structure on the underlying manifold, we get potentially different bounded volume classes, and the goal of this talk will be to explain how these bounded classes change as the quasiisometry type of the hyperbolic structure changes. Along the way, we will contemplate the classification of Kleinian groups by their end invariants and explore some interesting (bizarre) properties of bounded cohomology. 
Oct 9  No Seminar  No Seminar 
Oct 16 at 3pm  Daniel Woodhouse  Revisiting Leighton’s graph covering theorem
Abstract: Leighton’s graph covering theorem states that two finite graphs with isomorphic universal covers have isomorphic finite covers. I will discuss a new proof that involves using the Haar measure to solve a set of gluing equations. I will discuss generalizations to graphs with fins, and applications to quasiisometric rigidity. 
Oct 16 at 4:30pm  Emily Stark  Cannon–Thurston maps in nonpositive curvature
Abstract: Two farreaching methods for studying the geometry of a finitely generated group with nonpositive curvature are (1) to study the structure of the boundaries of the group, and (2) to study the structure of its finitely generated subgroups. Cannon–Thurston maps, named after foundational work of Cannon and Thurston in the setting of fibered hyperbolic 3manifolds, allow one to combine these approaches. Mitra (Mj) generalized work of Cannon and Thurston to prove the existence of Cannon–Thurston maps for normal hyperbolic subgroups of a hyperbolic group. Such Cannon–Thurston maps can be used to obtain structure on the boundary of certain hyperbolic groups. I will explain why similar theorems fail for certain CAT(0) groups. This is joint work with Beeker–Cordes–Gardham–Gupta. 
Oct 23  TBA
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Oct 30  Thomas Koberda  TBA
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Nov 6  Yulan Qing  TBA
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Nov 13  TBA
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Nov 20  Valentina Disarlo  TBA
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Nov 27  TBA
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Dec 4  TBA
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Dec 11  Jen Taback and Rob Kropholler  TBA
Abstract:TBA 