$\newcommand{\Sp}{\operatorname{Sp}} \newcommand{\SL}{\operatorname{SL}} \newcommand{\GL}{\operatorname{GL}} \newcommand{\PGL}{\operatorname{PGL}} \newcommand{\SO}{\operatorname{SO}} \newcommand{\SU}{\operatorname{SU}} \newcommand{\PU}{\operatorname{PU}} \newcommand{\Pin}{\operatorname{Pin}} \newcommand{\Vol}{\operatorname{Vol}} \newcommand{\Aut}{\operatorname{Aut}} \newcommand{\Out}{\operatorname{Out}} \newcommand{\vcd}{\operatorname{vcd}} \newcommand{\Id}{\operatorname{Id}} \newcommand{\Flat}{\operatorname{Flat}} \newcommand{\CP}{\mathbb{CP}} \newcommand{\CC}{\mathbb{C}} \newcommand{\EE}{\mathbb{E}} \newcommand{\HH}{\mathbb{H}} \newcommand{\RR}{\mathbb{R}} \newcommand{\QQ}{\mathbb{Q}} \newcommand{\ZZ}{\mathbb{Z}} \newcommand{\calG}{\mathcal{G}} \newcommand{\calO}{\mathcal{O}} \newcommand{\from}{\colon} \newcommand{\cross}{\times}$

# Geometry and Topology Seminar

## Warwick Mathematics Institute, Term III, 2018-2019

 Thursday April 25, 15:00, room MS.04 None (None) None Abstract: None

 Thursday May 2, 15:00, room MS.04 Marko Berghoff (Humboldt University, Berlin) Moduli spaces of colored graphs Abstract: Moduli spaces of graphs show up not only in mathematics, for instance in geometric group theory or tropical geometry, but also in the study of Feynman integrals in quantum field theory. The latter case demands graphs to be equipped with additional data, such as directed and/or colored edges or restrictions on vertex types. This leads to moduli spaces with rich and interesting combinatorial/topological structures. In this talk I will focus on the case of hairy graphs with colored edges. Although the number of cells in the resulting moduli spaces grows "rather quickly" with the number of allowed colors, their topological properties stabilize in a controlled manner. I will discuss this and some other (conjectured) features in detail, and if time permits finish with comments on possible applications.

 Thursday May 9, 15:00, room MS.04 Weiwei Wu (Georgia) Semi-toric spherical systems and symplectomorphism groups Abstract: We will explain a generalization of semi-toric systems. In dimension four, such systems can be easily obtained by generalizing the notion of "toric blow-up". As it turns out, this construction gains new understandings of the symplectic mapping class groups. We will explain its relation to a long-standing question between Lagrangian Dehn twists and symplectic mapping class groups of rational manifolds, and potential construction of exotic finite group actions. This talk is based on several on-going joint works with Liat Kessler, Jun Li and Tian-Jun Li.

 Thursday May 16, 15:00, room MS.04 Henry Segerman (Oklahoma) From veering triangulations to pseudo-Anosov flows Abstract: Agol introduced veering triangulations of mapping tori, whose combinatorics are canonically associated to the pseudo-Anosov monodromy. In unpublished work, Guéritaud and Agol generalise an alternative construction to any closed manifold equipped with a pseudo-Anosov flow without perfect fits. Schleimer and I build the reverse map: from a transverse veering triangulation we canonically construct a dynamic pair in the sense of Mosher, which implies a combinatorial version of a pseudo-Anosov flow without perfect fits. I will also talk about work with Giannopolous and Schleimer building a census of transverse veering triangulations. The current census lists all transverse veering triangulations with up to 16 tetrahedra, of which there are 87,047. The number approximately doubles with each added tetrahedron.

 Thursday May 16, 16:00, room MS.04 Mark Bell (Independent) The Nielsen realisation and the conjugacy problems Abstract: We will discuss progress towards implementing a polynomial-time solution to the conjugacy problem for mapping class groups. In particular we will discuss how these tools and techniques lead to a new implementation of a solution to the Nielsen realisation problem. This is based on joint work with Richard Webb.

 Thursday May 23, 15:00, room MS.04 Agelos Georgakopoulos (Warwick) Planar Cayley graphs and Kleinian groups Abstract: Kleinian groups are a classical topic. I will give an overview and explain their relationship to groups having planar Cayley graphs. Moreover, I will show that if a finitely generated group $G$ acts faithfully and properly discontinuously by homeomorphisms on a planar surface, then $G$ admits such an action that is in addition co-compact.

 Thursday May 30, 15:00, room MS.04 Ian Frankel (HSE) Quantitatively recurrent Teichmüller geodesics Abstract: Geodesic flow for the Teichmüller metric on the moduli space of Riemann surfaces displays some key properties of geodesic flow on hyperbolic space, but the analogy is not perfect. For example, there are some rare instances in which pairs of geodesics "heading to the same point on the sphere at infinity" do not converge to each other exponentially quickly, or even at all. We will describe how geodesics that return to a compact part of the moduli space often are guaranteed to approach each other more quickly. Basic hyperbolic geometry, the definition of Teichmüller space, and the statement of Teichmüller's existence and uniqueness theorem are sufficient prerequisites for this talk.

 Thursday June 6, 15:00, room MS.04 TBA (TBA) TBA Abstract: TBA

 Thursday June 13, 15:00, room MS.04 David Futer (Temple) Special covers of alternating links Abstract: The "virtual conjectures” in low-dimensional topology, stated by Thurston in 1982, postulated that every hyperbolic 3-manifold has finite covers that are Haken and fibered, with large Betti numbers. These conjectures were resolved in 2012 by Agol and Wise, using the machine of special cube complexes. Since that time, many mathematicians have asked how big a cover one needs to take to ensure one of these desired properties. We begin to give a quantitative answer to this question, in the setting of alternating links in $S^3$. If an alternating link $L$ has a diagram with $n$ crossings, we prove that the complement of $L$ has a special cover of degree less than $n!$. As a corollary, we bound the degree of the cover required to get Betti number at least $k$. This is joint work with Edgar Bering.

 Thursday June 20, 15:00, room MS.04 TBA (TBA) TBA Abstract: TBA

 Thursday June 27, 15:00, room MS.04 TBA (TBA) TBA Abstract: TBA

Information on past talks. This line was last edited 2019-01-11.