Skip to main content

Graphs, surfaces, and cube complexes

9–13 July 2018

Organisers: Piotr Przytycki, Michah Sageev, Brian Bowditch

Registration is not yet open.

Symposium Poster

Workshop Poster

Schedule, Titles and Abstracts

Cube complexes, particularly those that satisfy a form of non-positive curvature called the $CAT(0)$ condition, have played a major role in recent work in geometry and low-dimensional topology. They were a vital tool in the celebrated work of Agol and Wise proving Thurston's virtual fibring conjecture. They feature prominently in the study of decompositions of groups into graphs of groups. Combinatorially, they are the realisation spaces of discrete median algebras, and as such have been studied from the point of view both of combinatorics and of lattice theory. They have also found applications to understanding the coarse geometry of the mapping class group and Teichmüller spaces, which have recently been shown to have a natural coarsely cubical structure.

There is considerable potential for interaction between researchers who have studied such structures from differing perspectives, and who have diverse insights into the subject. The purpose of this workshop is to mine this potential to solve old problems, such as whether $CAT(0)$ cube complexes with cocompact actions can contain periodic flats, and to develop it in new directions. These include studying other combinatorial structures which arise in low-dimensional topology such as the arc and curve complexes associated to a surface, where the combinatorial notion of ''dismantlability," borrowed from graph theory has begun to be used profitably. There is also direct interaction with the study of outer automorphism groups, via spaces made of $CAT(0)$ cube complexes with fundamental group a given right-angled Artin group, and via complexes such as the free splitting and free factor complexes.


Aerial photograph of Maths Houses

See also:
Mathematics Research Centre
Mathematical Interdisciplinary Research at Warwick (MIR@W)
Past Events 
Past Symposia 

Internet Access at Warwick:
Where possible, visitors should obtain an EDUROAM account from their own university to enable internet access whilst at Warwick.
If you need WiFi whilst at Warwick, click here for instructions (upon arrival at Warwick)
You can register for any of the symposia or workshops online. To see which registrations are currently open and to submit a registration, please click here.
Mathematics Research Centre
Zeeman Building
University of Warwick
Coventry CV4 7AL - UK