Tom Bourne
Office 226
Mathematical Institute
University of St Andrews
North Haugh
St Andrews
Fife
KY16 9SS
tom.bourne@standrews.ac.uk
+44 (0)1334 463731
I am a former research student (PhD) in the School of Mathematics and Statistics at the University of St Andrews. I was funded by EPSRC and was under the supervision of Professor Nik Ruškuc and Dr Colva RoneyDougal. My research interests include formal language theory, algebraic automata theory, and combinatorial semigroup theory. I was a member of the Algebra & Combinatorics research group and the Centre for Interdisciplinary Research in Computational Algebra (CIRCA).
Away from maths, I enjoy listening to, composing, and performing music, and I hold a performance diploma (DipLCM) awarded by the London College of Music. I am also a qualified ASA/UKCC Level 2 swimming coach, formerly volunteering at Step Rock ASC.
Academic Qualifications
Postgraduate Studies (current)
Mathematics (PhD)
University of St Andrews, Scotland, UK; 2013  2017
Thesis: Counting Subwords and Other Results Related to the Generalised StarHeight Problem
Supervisors: Professor Nik Ruškuc and Dr Colva RoneyDougal
Undergraduate Studies
Master of Mathematics (MMath), First Class Honours (81%)
University of York, England, UK; 2009  2013
Final Year Project: Inverse Semigroups and Inductive Groupoids
Supervisor: Professor Victoria Gould
Professional Accreditation
Associate Member of the Institute of Mathematics and its Applications
Associate Fellow of the Higher Education Academy
Professional Development
Introduction to University Teaching 1: Supporting Student Learning (ID5101)
Introduction to University Teaching 2: Curriculum Design and Assessment (ID5102)
Other Qualifications
Diploma of the London College of Music (DipLCM) in Electronic Keyboard Performance
UKCC Level 2 Certificate for Coaching Swimming
ASA Level 1 Certificate for Teaching Swimming
Sports Leader UK Level 1 Award in Sports Leadership
Emergency First Aid at Work
My main areas of research are formal language theory, algebraic automata theory, and combinatorial semigroup theory. My research interests mainly revolve around the generalised starheight problem, of which you can find a detailed account on JeanÉric Pin's personal homepage. I am also interested in grammars, cryptography and category theory.
Publications
Accepted

On the starheight of subword counting languages and their relationship to Rees zeromatrix semigroups.
Joint with Nik Ruškuc; Theoretical Computer Science 653 (2016) pp. 8796; DOI; arXiv.
Conferences
Organisation
August 2016: Young Researchers in Mathematics (YRM) 2016 at the University of St Andrews.
Attended
April 2017: The British Colloquium for Theoretical Computer Science at the University of St Andrews.
April 2017: The Scottish Combinatorics Meeting 2017 at the University of St Andrews.
June 2016: The International Conference on Semigroups and Automata 2016 at the University of Lisbon.
April 2016: The Scottish Combinatorics Meeting 2016 at the University of Glasgow.
March 2016: The twentythird NBSAN meeting at the University of St Andrews.
August 2015: Young Researchers in Mathematics (YRM) 2015 at the University of Oxford.
June 2015: AMSEMSSPM International Meeting 2015 at the University of Porto.
June 2015: Workshop on Groups and Semigroups at the University of Porto.
April 2015: The twentieth NBSAN meeting at the University of St Andrews.
January 2015: The nineteenth NBSAN meeting at the University of York.
July 2014: The eighteenth NBSAN meeting at the University of Edinburgh.
June/July 2014: Young Researchers in Mathematics (YRM) 2014 at the University of Warwick.
June 2014: The EMS Postgraduate Meeting 2014 at the Burn House, Edzell.
November 2012: The thirteenth NBSAN meeting at the University of York.
Talks
Invited
April 2017: CIRCA Lunch Seminar, University of St Andrews
You want me to count the arrows? I'll \( C_{2} \) it! [slides]
October 2016: York Semigroup, University of York
Subwords and Stars [slides]
April 2015: The twentieth NBSAN Meeting, University of St Andrews
Tackling the Generalized StarHeight Problem [slides]
April 2015: CIRCA Lunch Seminar, University of St Andrews
The Generalized StarHeight Problem [slides]
Contributed
April 2017: British Colloquium for Theoretical Computer Science 2017, University of St Andrews
Subwords and Stars [slides]
April 2017: Pure Postgraduate Seminar (PPS), University of St Andrews
English, French, Spanish... A Variety of Languages
January 2017: Postgraduate Intradisciplinary Mathematics Symposium (PIMS) 2017, Burn House, Edzell
Finite State Automata
January 2017: School of Mathematics & Statistics Research Day, University of St Andrews
Formal Languages and Automata [slides]
December 2016: PPS, University of St Andrews
Subwords and Stars [slides]
April 2016: PPS, University of St Andrews
You want me to count the arrows? I'll \( C_{2} \) it! [slides]
January 2016: PIMS 2016, Burn House, Edzell
Counting Stars [slides]
November 2015: PPS, University of St Andrews
Semigroups, Subwords and StarHeight [slides]
August 2015: Young Researchers in Mathematics (YRM) 2015, University of Oxford
Combinatorics on Words [slides]
January 2015: PIMS 2015, Burn House, Edzell
An Introduction to Algebra [slides]
October 2014: PPS, University of St Andrews
Multilingual Monoids: Why Study Varieties of Languages? [slides]
June 2014: EMS Postgraduate Meeting, Burn House, Edzell
Formal Languages and the Generalized StarHeight Problem [slides]
March 2014: PPS, University of St Andrews
Minimal Automata and the Method of Quotients [slides]
January 2014: PIMS 2014, Burn House, Edzell
The Generalized StarHeight Problem [slides]
December 2013: PPS, University of St Andrews
Inverse Semigroups and Inductive Groupoids [slides]
Outreach
November 2016: Royal Institution Mathematics Masterclasses (Edinburgh and Lothian), HeriotWatt University
Formal Languages and Automata [slides]
September 2016: Postgraduate Researcher Induction Day, University of St Andrews
Learning to Juggle: Adadpting to PhD Life
September 2015: Postgraduate Researcher Induction Day, University of St Andrews
Learning to Juggle: Adadpting to PhD Life
Academic Year 2016/17
Semester 1
MT2000Workshop (Python Computing Workshop for 2000Level MT Modules)
MT2501 (Linear Mathematics) — 3 tutorials every other week.
MT3501 (Linear Mathematics 2) — 2 tutorials per week.
Semester 2
MT1002 (Mathematics) — computing project supervision.
MT2501 (Linear Mathematics) — 2 examples classes every other week.
MT2505 (Abstract Algebra) — 2 tutorials every other week.
MT2507 (Mathematical Modelling) — computing project supervision.
MT3852 (Automata, Languages and Complexity) — 1 tutorial per week and informal administrative duties.
Academic Year 2015/16
Semester 1
MT2501 (Linear Mathematics) — 2 tutorials every other week.
MT3501 (Linear Mathematics 2) — 3 tutorials per week.
Semester 2
MT1003 (Pure and Applied Mathematics) — 2 tutorials per week.
MT2507 (Mathematical Modelling) — computing project supervision and marking.
Academic Year 2014/15
Semester 1
MT1002 (Mathematics) — computing project supervision and marking.
MT2501 (Linear Mathematics) — 4 tutorials and 1 examples class in alternating weeks.
Semester 2
MT1002 (Mathematics) — computing project supervision.
MT2501 (Linear Mathematics) — 3 tutorials and 2 examples classes in alternating weeks.
Academic Year 2013/14
Semester 1
MT1002 (Mathematics) — 2 tutorials per week.
MT2002 (Algebra and Analysis) — computing project supervision.
Semester 2
MT1002 (Mathematics) — 2 tutorials per week and computing project supervision.
Mathematical Institute Risk League
The Mathematical Institute Risk League is a league played amongst PhD students in the School of Mathematics and Statistics at the University of St Andrews. In order to play, we use a Risk clone called Gambit which can be found at gamesbyemail.com. If you are interested in joining the next season then you should contact the Risk Convenor, Michael Torpey, either in person or at mct25@standrews.ac.uk.
Summer 2016
This current season consists of 9 players each playing 12 games over the course of 6 weeks. In this league, 6player games are worth 2 points while 3player games are worth 1 point.
League Table
Points  6player (Won/Played)  3player (Won/Played)  

1  Bourne  10  4/8  2/4 
2  Allanson  8  3/8  2/4 
3  Hodgson  6  2/8  2/4 
4  Hatfield  5  2/8  1/4 
5  Torpey  3  1/8  1/4 
6  Troscheit  2  0/8  2/4 
=7  Macfarlane  1  0/8  1/4 
=7  McDevitt  1  0/8  1/4 
9  Khalid  0  0/8  0/4 
Fixtures
Week 1 (w/c 27th June) 
Alpha  Allanson/Bourne/Hatfield 
Beta  Hod/Kha/Mac/McD/Tor/Tro  
Gamma  Hodgson/Khalid/Macfarlane  
Delta  All/Bou/Hat/McD/Tor/Tro  
Week 2 (w/c 4th July) 
Alpha  McDevitt/Torpey/Troscheit 
Beta  All/Bou/Hat/Hod/Kha/Mac  
Gamma  Allanson/Hodgson/McDevitt  
Delta  Bou/Hat/Kha/Mac/Tor/Tro  
Week 3 (w/c 11th July) 
Alpha  Bourne/Khalid/Torpey 
Beta  All/Hat/Hod/Mac/McD/Tro  
Gamma  Hatfield/Macfarlane/Troscheit  
Delta  All/Bou/Hod/Kha/McD/Tor  
Week 4 (w/c 18th July) 
Alpha  Allanson/Khalid/Troscheit 
Beta  Bou/Hat/Hod/Mac/McD/Tor  
Gamma  Bourne/Macfarlane/McDevitt  
Delta  All/Hat/Hod/Kha/Tor/Tro  
Week 5 (w/c 25th July) 
Alpha  Hatfield/Hodgson/Torpey 
Beta  All/Bou/Kha/Mac/McD/Tro  
Gamma  Allanson/Macfarlane/Torpey  
Delta  Bou/Hat/Hod/Kha/McD/Tro  
Week 6 a.k.a YRM Week (w/c 1st August) 
Alpha  Bourne/Hodgson/Troscheit 
Beta  All/Hat/Kha/Mac/McD/Tor  
Gamma  Hatfield/Khalid/McDevitt  
Delta  All/Bou/Hod/Mac/Tor/Tro 
Winter 2015/16
This season consisted of 8 players each playing 17 games over the course of 7 weeks.
League Table
Played  Points  

1  Allanson  17  6** 
2  Bourne  17  5* 
=3  Hodgson  17  5 
=3  Torpey  17  5 
5  Wilson  17  4* 
6  Troscheit  17  4 
7  McDevitt  17  2 
8  Macfarlane  17  1 
Asterisks (*) denote a Gamma win, and are used to determine a player's final position in the event of tied positioning.
Fixtures
Alpha  Beta  Gamma  
Week 1 (w/c 11th January) 
1  All/Bou/Hod/Mac  McD/Tor/Tro/Wil  
2  All/Hod/McD/Tro  Bou/Mac/Tor/Wil  
Week 2 (w/c 18th January) 
1  All/Mac/McD/Wil  Bou/Hod/Tor/Tro  
2  All/Bou/McD/Tor  Hod/Mac/Tro/Wil  
Week 3 (w/c 25th January) 
1  All/Hod/Tor/Wil  Bou/Mac/McD/Tro  
2  All/Mac/Tor/Tro  Bou/Hod/McD/Wil  
One week hiatus due to GamesByEmail.com downtime.  
Week 4 (w/c 8th February) 
1  All/Bou/Tro/Wil  Hod/Mac/McD/Tor  Wilson 
2  All/Bou/Hod/Mac  McD/Tor/Tro/Wil  
Week 5 (w/c 15th February) 
1  All/Hod/McD/Tro  Bou/Mac/Tor/Wil  Bourne 
2  All/Mac/McD/Wil  Bou/Hod/Tor/Tro  
Week 6 (w/c 22nd February) 
1  All/Bou/McD/Tor  Hod/Mac/Tro/Wil  Allanson 
2  All/Hod/Tor/Wil  Bou/Mac/McD/Tro  
Week 7 (w/c 29th February) 
1  All/Mac/Tor/Tro  Bou/Hod/McD/Wil  Allanson 
2  All/Bou/Tro/Wil  Hod/Mac/McD/Tor 
Summer 2015
This season consisted of 7 players each playing 15 games over the course of 7 weeks.
League Table
Played  Points  

1  Elsden  15  8 
2  Hodgson  15  7 
3  Allanson  15  5 
=4  Baynes  15  4 
=4  Bourne  15  4 
=4  Hatfield  15  4 
7  Torpey  15  3 
Fixtures
Week 1 (w/c 22nd June) 
Alpha  Allanson/Baynes/Bourne 
Beta  Allanson/Elsden/Hatfield  
Gamma  Allanson/Hodgson/Torpey  
Delta  Baynes/Elsden/Hodgson  
Epsilon  Bourne/Hatfield/Torpey  
Week 2 (w/c 29th June) 
Alpha  Allanson/Baynes/Elsden 
Beta  Allanson/Bourne/Hodgson  
Gamma  Baynes/Bourne/Hatfield  
Delta  Baynes/Hodgson/Torpey  
Epsilon  Elsden/Hatfield/Torpey  
Week 3 (w/c 6th July) 
Alpha  Allanson/Baynes/Torpey 
Beta  Allanson/Bourne/Hatfield  
Gamma  Baynes/Bourne/Elsden  
Delta  Bourne/Hodgson/Torpey  
Epsilon  Elsden/Hatfield/Hodgson  
Week 4 (w/c 13th July) 
Alpha  Allanson/Bourne/Torpey 
Beta  Allanson/Elsden/Hodgson  
Gamma  Baynes/Elsden/Torpey  
Delta  Baynes/Hatfield/Hodgson  
Epsilon  Bourne/Elsden/Hatfield  
Week 5 (w/c 20th July) 
Alpha  Allanson/Baynes/Hodgson 
Beta  Allanson/Hatfield/Torpey  
Gamma  Baynes/Elsden/Hatfield  
Delta  Bourne/Elsden/Torpey  
Epsilon  Bourne/Hatfield/Hodgson  
Week 6 (w/c 27th July) 
Alpha  Allanson/Bourne/Elsden 
Beta  Allanson/Hatfield/Hodgson  
Gamma  Baynes/Bourne/Hodgson  
Delta  Baynes/Hatfield/Torpey  
Epsilon  Elsden/Hodgson/Torpey  
Week 7 (w/c 3rd August) 
Alpha  Allanson/Baynes/Hatfield 
Beta  Allanson/Elsden/Torpey  
Gamma  Baynes/Bourne/Torpey  
Delta  Bourne/Elsden/Hodgson  
Epsilon  Hatfield/Hodgson/Torpey 
Winter 2014/15
This season consisted of 6 players each playing 10 games over the course of 5 weeks.
League Table
Played  Points  

1  Allanson  15  8* 
2  Baynes  15  6** 
3  Elsden  15  5 
4  Hodgson  15  3* 
5  Bourne  15  2* 
6  Torpey  15  1 
Asterisks (*) denote a Gamma win, and were used to determine a player's final position in the event of tied positioning.
Fixtures
Alpha  Beta  Gamma  
Week 1 (w/c 17th November) 
1  Allanson/Baynes/Bourne  Elsden/Hodgson/Torpey  Hodgson 
2  Allanson/Bourne/Hodgson  Baynes/Elsden/Torpey  
Week 2 (w/c 24th November) 
1  Allanson/Baynes/Elsden  Bourne/Hodgson/Torpey  Allanson 
2  Allanson/Bourne/Torpey  Baynes/Elsden/Hodgson  
Week 3 (w/c 1st December) 
1  Allanson/Baynes/Hodgson  Bourne/Elsden/Torpey  Bourne 
2  Allanson/Elsden/Hodgson  Baynes/Bourne/Torpey  
Week 4 (w/c 8th December) 
1  Allanson/Baynes/Torpey  Bourne/Elsden/Hodgson  Baynes 
2  Allanson/Elsden/Torpey  Baynes/Bourne/Hodgson  
Week 5 (w/c 15th December) 
1  Allanson/Bourne/Elsden  Baynes/Hodgson/Torpey  Baynes 
2  Allanson/Hodgson/Torpey  Baynes/Bourne/Elsden 
Summer 2014
This inaugural season consisted of 8 players each playing 14 games over the course of 7 weeks.
League Table
Played  Points  

=1  Baynes  14  6 
=1  Jonusas  14  6 
=3  Elsden  14  5 
=3  Hodgson  14  5 
5  Bourne  14  4 
6  Allanson  14  2 
=7  Troscheit  14  0 
=7  Syntelis  14  0 
Fixtures
Alpha  Beta  
Week 1 (w/c 26th May) 
1  Allanson/Baynes/Bourne/Elsden  Hodgson/Jonusas/Syntelis/Troscheit 
2  Allanson/Bourne/Hodgson/Syntelis  Baynes/Elsden/Jonusas/Troscheit  
Week 2 (w/c 2nd June) 
1  Allanson/Elsden/Hodgson/Troscheit  Baynes/Bourne/Jonusas/Syntelis 
2  Allanson/Baynes/Hodgson/Jonusas  Bourne/Elsden/Syntelis/Troscheit  
Week 3 (w/c 9th June) 
1  Allanson/Bourne/Jonusas/Troscheit  Baynes/Elsden/Hodgson/Syntelis 
2  Allanson/Elsden/Jonusas/Syntelis  Baynes/Bourne/Hodgson/Troscheit  
One week hiatus for catchup from conferences/holidays.  
Week 4 (w/c 23rd June) 
1  Allanson/Baynes/Syntelis/Troscheit  Bourne/Elsden/Hodgson/Jonusas 
2  Allanson/Baynes/Bourne/Elsden  Hodgson/Jonusas/Syntelis/Troscheit  
Week 5 (w/c 30th June) 
1  Allanson/Bourne/Hodgson/Syntelis  Baynes/Elsden/Jonusas/Troscheit 
2  Allanson/Elsden/Hodgson/Troscheit  Baynes/Bourne/Jonusas/Syntelis  
Week 6 (w/c 7th July) 
1  Allanson/Baynes/Hodgson/Jonusas  Bourne/Elsden/Syntelis/Troscheit 
2  Allanson/Bourne/Jonusas/Troscheit  Baynes/Elsden/Hodgson/Syntelis  
Week 7 (w/c 14th July) 
1  Allanson/Elsden/Jonusas/Syntelis  Baynes/Bourne/Hodgson/Troscheit 
2  Allanson/Baynes/Syntelis/Troscheit  Bourne/Elsden/Hodgson/Jonusas 