Projects per year
Personal profile
Personal Statement
My research interests are in geometric methods in combinatorial group theory, semigroup theory, applied topology, and mathematical formalisation. I obtained my PhD from the Univeristy of Glasgow in 2008 under the supervision of Prof. Stephen J. Pride. I joined the University of Strathclyde in that year as a Teaching Assistant and I am now a Teaching Fellow. Between 2011 and 2018 I was the Manager of the University's Maths Skills Support Centre.
I am a Senior Fellow of the Higher Education Academy and an Ordinary Member of the Edinburgh Mathematical Society. I sat on the society's Education Committee between 2016 and 2024. I am currently the Year 5 Coordinator for the Department of Mathematics and Statistics and was previsouly the department's Chief Undergraduate Academic Selector, Year 1 Coordinator, UG SSLC Convenor and Directory of Teaching.
Teaching Interests
In 2026/27 I will be teaching:
- MM143 Mathematical Foundations
- MM359 Algebraic Structures
Previous teaching:
- MM101 Introduction to Calculus
- MM103 Geometry and Algebra with Applications
- MM105 Applications of Mathematics
- MM112 Mathematics 2B
- MM113 Mathematics 1E
- MM114 Mathematics 2E
- MM116 Mathematics 1C
- MM117 Mathematics 1D
- MM125 Mathematics Summer School
- MM202 Advanced Calculus
- MM211 Mathematics 3B
- MM213 Engineering Mathematics 3E
- MM215 Mathematics 2D
- MM217 Mathematics 2M
- MM311 Mathematics 4B
I have supervised a number of level 4 honours projects in topics such as topology, theory of automata, complex dynamics, geometry, knot theory, number theory and group theory.
Research Interests
I am interested in a number of areas in combinatorial group theory and semigroup theory:
- the word problem for finitely presented group
- Dehn functions of groups
- asphericity of relative group presentations
- groups defined by finite state automata
- inverse semigroups
More recently, I have been investigating how to use the formal proof assistant Lean4 in mathematical education.
I am also interested in pedagogical research in the mathematical sciences, particularly in areas related to mathematics and satistics support.
Academic / Professional qualifications
Senior Fellow of the Higher Education Academy (August 2019).
External positions
Education Committee Member, Edinburgh Mathematical Society
2016 → 2024
Keywords
- Combinatorial Group Theory
- Geometric Group Theory
- Semigroup Theory
- Mathematics and Statistics Support
- Mathematical Formalisation
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Collaborations and top research areas from the last five years
Recent external collaboration on country/territory level. Dive into details by clicking on the dots or
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Creative Knowledge Exchange: Engagement Between Mathematics, Biomedical Engineering and the Creative Arts
Dombi, E. (Principal Investigator), Banas, N. (Co-investigator), Davidson, P. (Co-investigator), Devlin, J. (Co-investigator), Kelly, L. (Co-investigator), Kleczkowski, A. (Co-investigator), McLeay, A. (Co-investigator) & Witte, K. (Co-investigator)
15/12/25 → 28/02/26
Project: Knowledge Exchange
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β-diversity and graph sheaf Laplacians
Davidson, P. & Grinfeld, M., 24 Jan 2026, 7 p.Research output: Working paper/Preprint/Pre-registration › Working Paper/Preprint
Open Access -
A Template for Accessible Lecture Notes
Davidson, P., 13 Aug 2024, Glasgow: University of Strathclyde, 11 p.Research output: Working paper/Preprint/Pre-registration › Guide or manual
Open AccessFile10 Downloads (Pure)
Activities
- 4 Organiser of special symposia
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PRIMES: Pedagogy and Practice in Mathematics Education Scotland
Corson, L. (Organiser), Coutts, E. (Organiser), Ahmed, S. (Speaker), Kelly, L. (Speaker), Coutts, E. (Speaker), Corson, L. (Speaker), McPike, R. (Speaker) & Davidson, P. (Speaker)
27 Mar 2026Activity: Presenting or Organising an Event › Organiser of special symposia
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Mathematics and Statistics Teaching Away Day
Watret, C. (Organiser), McLeay, A. (Organiser), Corson, L. (Invited speaker), Miller, A. (Invited speaker), Watret, C. (Invited speaker), Roberts, A. (Invited speaker), Kelly, L. (Participant), Dombi, E. (Participant), Csoban, T. (Participant), Stewart, R. (Participant), Devlin, J. (Participant), McPike, R. (Participant), Davidson, P. (Participant) & Miller, B. H. (Participant)
19 May 2025Activity: Presenting or Organising an Event › Organiser of special symposia