Mark C Bell

My research focuses on computational problems in low-dimensional topology. In particular decision problems in mapping class groups of surfaces.

I now work in industry, but prior to this I was a J. L. Doob Research Assistant Professor at the University of Illinois and then a Visiting Fellow at the University of Warwick as part of their 2017/18 EPSRC Symposium on Geometry, Topology and Dynamics in Low Dimensions. In the past I have also done work with the National Center for Supercomputing Applications and the Illinois Geometry Lab.

Here are some of the upcoming things that I will be involved in:

You can also find some of the things I have previously been involved with.


I have written several pieces of software including:

  • Twister constructs triangulations of surface bundles over the circle and Heegaard splittings.

  • Flipper decides the Nielsen–Thurston type of a given mapping class and, for pseudo-Anosov mapping classes, constructs a layered, veering triangulation of their mapping torus, as described by Agol.

  • Curver for performing calculations in the curve complex.

  • Bigger for performing calculations with big mapping classes on infinite-type surfaces.

If you need to give me access to something, try creating an account for me and installing one of my public keys.


Papers I have written can be found on the arXiv. This includes:

  • The flow group of rooted abelian or quadratic differentials

  • Experimental statistics for Mirzakhani’s Theorem

  • Coding Teichmüller flow using veering triangulations

  • Computing trisections of 4-manifolds

  • Cubical Geometry in the Polygonalisation Complex

  • Polynomial-time algorithms for curve graphs

  • Asymmetric dynamics of outer automorphisms

  • Applications of fast triangulation simplification

  • Simplifying triangulations

  • Slow north-south dynamics on PML

  • The pseudo-Anosov and conjugacy problems are in NP and co-NP

  • Deciding reducibility of mapping classes is in NP

  • The monodromies of homogeneous links