Fall 2018 GGD Workshop

Titles and Abstracts

Marissa Loving

Title: Least dilatation of pure surface braids

Abstract: The n-stranded pure surface braid group of a genus g surface can be described as the subgroup of the pure mapping class group of a surface of genus g with n-punctures which becomes trivial on the closed surface. I am interested in the least dilatation of pseudo-Anosov pure surface braids. For the n=1 case, upper and lower bounds on the least dilatation were proved by Dowdall and Aougab—Taylor, respectively. In this talk, I will describe the upper and lower bounds I have proved as a function of g and n.

Ryan Spitler

Title: Profinite Completions and Representations of Groups

Abstract: The profinite completion of a group G, encodes all of the information of the finite quotients of G. A residually finite group G is called profinitely rigid if any other residually finite group with an isomorphic profinite completion is itself necessarily isomorphic to G. I will discuss some ways that the profinite completion can be used to understand linear representations of G and applications to questions related to profinite rigidity. In particular, I will explain the role this plays in forthcoming work with Bridson, McReynolds, and Reid which establishes the profinite rigidity of the fundamental groups of certain hyperbolic 3-manifolds and orbifolds.

Shi Wang

Title: Homological norms on nonpositively curved manifolds

Abstract: Gromov norm is a topological invariant that measures how efficiently a homology class can be represented by the linear combinations of singular simplices. In this talk, we relate the Gromov norm on homology classes to the harmonic norm on the dual cohomology and obtain double sided bounds in terms of the volume and other geometric quantities of the underlying manifolds. This extends the previous result of Brock and Dunfield.

William Worden

Title: Generic veering triangulations are not geometric.

Abstract: Every pseudo-Anosov mapping class f defines an associated veering triangulation T_f of a punctured mapping torus. We show that generically, T_f is not geometric. Here, the word “generic” can be taken either with respect to random walks in mapping class groups or with respect to counting geodesics in moduli space. After describing how veering triangulations are obtained from pseudo-Anosov maps, we will discuss some tools that go into the proof and give an outline if time permits.