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:
New perspectives in Computational Group Theory at the University of Warwick, 24th – 26th June 2024.
You can also find some of the things I have previously been involved with.
Software¶
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.
Writing¶
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