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

Geometry and Topology Seminar

Warwick Mathematics Institute, Term III, 2018-2019

Please contact Saul Schleimer if you would like to speak or to suggest a speaker.


Thursday April 25, 15:00, room MS.03

TBA (TBA)

TBA

Abstract: TBA


Thursday May 2, 15:00, room MS.03

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.03

Weiwei Wu (Georgia)

TBA

Abstract: TBA


Thursday May 16, 15:00, room MS.03

Henry Segerman (Oklahoma)

TBA

Abstract: TBA


Thursday May 23, 15:00, room MS.03

Agelos Georgakopoulos (Warwick)

TBA

Abstract: TBA


Thursday May 30, 15:00, room MS.03

Ian Frankel (HSE)

TBA

Abstract: TBA


Thursday June 6, 15:00, room MS.03

TBA (TBA)

TBA

Abstract: TBA


Thursday June 13, 15:00, room MS.03

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.03

TBA (TBA)

TBA

Abstract: TBA


Thursday June 27, 15:00, room MS.03

TBA (TBA)

TBA

Abstract: TBA



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