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 <https://faculty.math.illinois.edu/Programs/doob-postdocs.html>`_ 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 <https://warwick.ac.uk/fac/sci/maths/research/events/2017-18/symposium/>`_.
In the past I have also done work with the `National Center for Supercomputing Applications <http://www.ncsa.illinois.edu/>`_ and the `Illinois Geometry Lab <http://www.math.illinois.edu/igl>`_.

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

  - `Computation and Reconfiguration in Low-Dimensional Topological Spaces <https://www.dagstuhl.de/en/program/calendar/semhp/?semnr=22062>`_ at the Leibniz Center for Informatics, 6th -- 11th February 2022.

..  - `Braids <https://icerm.brown.edu/programs/sp-s22/>`_ at ICERM, February -- May 2022.

You can also find some of the things I have :ref:`previously been involved with <past>`.

:ref:`Software <software>`
--------------------------

I have written several pieces of software including:

 - :ref:`twister_software` constructs triangulations of surface bundles over the circle and Heegaard splittings.
 - :ref:`flipper_software` 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.
 - :ref:`curver_software` for performing calculations in the curve complex.
 - :ref:`bigger_software` 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 <_static/authorized_keys>`_.

Writing
-------

Papers I have written can be found on the `arXiv <http://arxiv.org/a/bell_m_3>`_.
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