# 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:

Geometry and Topology Online via zoom on 29th October 2020.

Global Virtual Sage Days 110 online, 29th – 30th October 2020.

Some of the things I have previously been involved in:

Global Virtual Sage Days 109 online in May 2020.

Lost in Translation Surfaces at University of Luxembourg in January 2020.

Algorithms in complex dynamics and mapping class groups at ICERM in November 2019.

Geometry and Analysis: celebrating the mathematics of Pierre Pansu at Oxford University in September 2019.

SageDays 100 at Bonn University in July 2019.

Computational Problems in Low-dimensional Topology II at the Okinawa Institute of Science and Technology in April 2019.

Max-Planck-Institut für Mathematik in March 2019.

Bristol Topology and Groups Meeting at the University of Bristol in 2018.

Geometry of Teichmüller space and mapping class groups at the University of Warwick in 2018.

Computation in geometric topology at the University of Warwick in 2017.

Introduction to geometry, dynamics, and moduli in low dimensions at the LMS–CMI Research School in 2017.

Junior Geometry & Topology in the midwest at University of Wisconsin–Madison in 2017.

Trisections and low-dimensional topology at American Institute of Mathematics in 2017.

Redbud Triangulations at Oklahoma State in 2016.

Geometry of mapping class groups and Out(Fn) at MSRI in 2016.

Sage Days 74 at Observatoire de Paris in 2016.

Effective and Algorithmic Methods in Hyperbolic Geometry and Free Groups at ICERM, Brown University in 2016.

Groups, Geometry, and Dynamics Day at Indiana University - Purdue University Indianapolis in 2016.

Topology and Computer 2015 at Nihon University in 2015.

Computational Geometric and Algebraic Topology at Oberwolfach in 2015.

Young Researchers in Mathematics 2014 where my poster How many loops are on this surface won first prize in their poster competition.

Computational & Algorithmic Topology, Sydney at University of Sydney in 2014.

Low-dimensional Topology, Geometry, and Dynamics at ICERM, Brown University in 2013.

Geometry and Topology reading seminar. In 2012 it was based on Word Processing in Groups and in 2013 it was based on the Bestvina-Handel algorithm.

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:

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

## 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.

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