Mark C Bell

I was a Visiting Fellow at the University of Warwick as part of their 2017/18 EPSRC Symposium on Geometry, Topology and Dynamics in Low Dimensions. Before that I was a J. L. Doob Research Assistant Professor at the University of Illinois.

In the past I have also done work with the National Center for Supercomputing Applications and the Illinois Geometry Lab.

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

Activities

Some of the upcoming things that I will be involved in:

Some of the things I have previously been involved in:

As well as some non-mathematical things:

  • PyCon UK 2017,

  • Cloud OnAir,

  • UK Manycore Developer Conference,

  • Scaling to Petascale Institute 2017,

  • XSEDE HPC Big Data Workshop,

  • GPU Programming Using OpenACC, and

  • Core Algorithms for High Performance Scientific Computing.

I have also given talks at: University of Glasgow; University of Wisconsin–Madison; Eastern Illinois University; Brown University; University of Toronto; Oklahoma State University; University of California, Santa Barbra; University of California, Davis; Mathematical Sciences Research Institute; Temple University; City University of New York; CIAS Paris; University of Illinois at Chicago; Institute for Advanced Study, Princeton; Indiana University – Purdue University Indianapolis; Nihon University; Mathematisches Forschungsinstitut Oberwolfach; Indiana University; University of Illinois; The University of Sheffield; University of Queensland; University of Sydney; ICERM; Toulouse Mathematics Institute; University of Cambridge; University of Bristol; Imperial College London; University of Warwick; and University of Southampton.

Writing

Some of the things I’ve written about can be found on the arXiv. This includes:

  • 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

Software

I have also 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.

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