Stuart Burrell
Carnegie PhD Scholar in Pure Mathematics

School of Mathematics and Statistics
University of St Andrews
St Andrews
KY16 9SS
United Kingdom

Phone: +44 (0) 1334 463744

Research interests
  • Fractal Geometry
  • Dimension Theory
  • Dynamical Systems


I am a doctoral researcher in pure mathematics at the University of St Andrews, funded by a Scholarship from the Carnegie Trust.

In 2016, I graduated from the University of St Andrews with a first class master's degree in pure mathematics. My current research will focus on fractal geometry and related fields in pure analysis, supervised by Dr Jonathan Fraser and Professor Kenneth Falconer.

A short CV is available here.

Awards and Scholarships
  • Open Data Science Conference (ODSC) Scholarship, London 2016
  • 2016 Institute of Mathematics Graduate Prize Winner
  • Carnegie PhD Scholarship, Tenure 2016-2020
  • Sanderson Prize, University of St Andrews, 2016
  • Arthur Hinton Read Memorial Prize, University of St Andrews, 2016
  • The Deans' List, University of St Andrews, 2013, 2014, 2015, 2016
  • Duncan Prize, University of St Andrews, 2016
  • Medal (Mathematics M.Math, Fourth/Fifth Level), University of St Andrews, 2016
  • The Principal's Scholarship for Academic Excellence, University of St Andrews, 2015
  • The University Scholarship for Research and Leadership, University of St Andrews, 2015
  • Laidlaw Scholar in Research and Leadership, 2015

  • Fractals and Dimensions, Institut Mittag-Leffler, Sweden, December 2017.
  • Estimating Animal Abundance and Density using Acoustic Data, University of Cape Town, South Africa, January 2017.
  • PAMTech Advanced PAMGuard, Edinburgh, 2016
  • CoDiMa Software Carpentry, International Centre for Mathematical Sciences, Edinburgh, 2016.
  • Spatial Capture-Recapture Methods, CREEM, St Andrews, 2016.

Conferences and Talks
  • Dimension of inhomogeneous attractors for conformal and affine iterated function systems, St Andrews, January 2018 (upcoming).
  • Inhomogeneous attractors and upper box dimension, Institut Mittag-Leffler, Sweden, December 2017, slides (delivered).
  • Introduction to trace contrast methods, Estimating animal abundance and density using acoustic data, South Africa, January 2017 (delivered).
  • Trace contrast methods in acoustic space, African Institute for Mathematical Sciences, South Africa, January 2017, slides (delivered).
  • SMSTC Symposium, Perth, 2016 (attended).
  • ODSC Machine Learning and Deep Learning Conference, London, 2016 (attended).
  • Sequential Monte Carlo in population dynamics, St Andrews, 2016, slides.

Academic and Professional Development

Teaching and Responsibilities
  • MT1002 Mathematics, Tutor and Microlab Demonstrator, Semester 1 2017/18
  • MT2508 Statistical Inference, Tutor, Semester 2 2016/17
  • MT1003 Pure and Applied Mathematics, Tutor, Semester 2 2016/17
  • MT2000 Python Workshop, Tutor, Semester 1 2016/17.
  • MT2504 Combinatorics and Probability, Tutor, Semester 1 2016/17.
  • Academic Tutor for the Centre for Academic and Professional Development, St Andrews
  • SMSTC Council Student Representative

Master's Theses

Software Contributions
  • GAP Semigroups package [1][2] : implemented methods for a decision algorithm for the order problem of natural and tropical matrix semigroups. [4][5][6][7][8]
  • GAP Digraphs package [1][3]: implementated methods including Johnson's algorithm for the computation of the simple circuits of a digraph. [4][9]

  • [1] The GAP Group. GAP -- Groups, Algorithms, and Programming, Version 4.8.3, 2016.
  • [2] J.D. Mitchell et al. Semigroups - GAP package, version 2.7.4, 2016. http://www.
  • [3] J. De Beule, J. JonuĊĦas, J. D. Mitchell, M. Torpey, and W. Wilson. Digraphs - GAP package, Version 0.5, March 2016.
  • [4] I. Simon A. Mandel. On Finite Semigroups of Matrices. Theoretical Computer Science, 5:101--111, 1977.
  • [5] S. Gaubert. On the Burnside problem for Semigroups of Matrices over the (max, +) Algebra. Semigroup Forum, 52:271--292, 1996.
  • [6] K.G. Farlow. Max-Plus Algebra, Master's thesis, Virginia Polytechnic Institute and State University, United States, 2009.
  • [7] I. Simon. Limited subsets of the free monoid. Proc. of the 19th Annual Symposium on Foundations of Computer Science, pages 143--150, 1978. IEEE.
  • [8] S.A. Burrell. The Order Problem for Natural and Tropical Matrix Semigroups in GAP, Master's thesis, University of St Andrews, United Kingdom, 2016.
  • [9] D.B. Johnson. Finding all the elementary circuits of a directed graph. SIAM J. Comput., 4(1):77--84, 1975.