This is the homepage of Alistair Wallis. I started a PhD at Heriot-Watt in September 2009. My main research interests lie in algebraic semigroup theory, geometric group theory, category theory, fractal geometry and non-commutative topology but I am also interested in combinatorics, probability theory, stochastic processes, statistics, mathematical physics, theoretical computer science and the philosophy and history of maths and science. My supervisor is Mark Lawson.

Previously, I did an MMath degree at St Andrews University from 2005 to 2009. I did research into the generating sets of infinite monoids and a Baire-categorical approach to typical properties of continuous functions in the summer of 2008. My master’s dissertation was about a mathematical framework for statistical inference in finite-dimensional quantum systems (pdf). In my first year at Heriot-Watt I took SMSTC courses in Algebra, Geometry and Topology, and Probability.

I have been Maths PhD rep at Heriot-Watt since 2010. Here are some useful links.

Conference Slides:

• Rees monoids, self-similar groups and fractals (NBSAN, St Andrews, 2011, slides)
• Patterns in fractals (The Burn, Edzell, 2011, slides)
• Rees monoids, automaton groups and functional programming (PGTC, Aberdeen, 2011, slides)

Other Slides and Notes:

• Introduction to Left Rees Monoids (slides)
• Gentle Introduction to Category Theory (slides)
• Statistics in Quantum Computing (slides)
• Fractal Geometry (with Nick Loughlin, now in Newcastle) (notes)
• Yoneda Lemma and Universality (slides) (scanned notes)
• Categories and Monoids (slides)
• Automatic Structures in Scala (slides)
• Molecular Symmetry and Electron Orbitals (slides)

Publications:

• J. T. Hyde, N. J. Loughlin, M. Quick, N. Ruskuc & A. R. Wallis, "On the growth of generating sets for direct powers of semigroups", Semigroup Forum Vol 84 Issue 1, pp116-130 (2012).
• M. V. Lawson, A. R. Wallis, "A Correspondence Between a Class of Monoids and Self-Similar Groups II" (in preparation)

Tutoring:

• Mulitvariable Calculus and Real Analysis A (Autumn 2009)
• Mathematics of Motion (Autumn 2009)
• Calculus B (Spring 2010)
• Stochastic Processes (Autumn 2010, 2011)
• Stochastic Modelling (Autumn 2010, 2011)
• Algebra A (Autumn 2010)
• Mulitvariable Calculus and Real Analysis B (Spring 2011, 2012)
• Introductory Mathematics (Autumn 2011)
• Introduction to Statistical Science B (Marking, Spring 2012)

From 2010 - 2012 I was the organiser of Friday afternoon PhD seminars. Here is the 2011/12 schedule.

I was previously a co-ordinator of category theory and (with Rob Stewart) functional programming reading groups.

Outside of maths, I love listening to music and playing the piano. My taste in music is insanely ecclectic, though mainly classical, jazz, rock, ska and "world music". I spent my final year at St Andrews heavily involved with organising live music events at the student's union, being on the committee of Musfund. In my third year at Heriot-Watt I was Treasurer of the HWU Whisky Tasting Society, performed in a pantomime adaptation of Sleeping Beauty and organised football matches every Thursday. While at St Andrews, I spent 3 years on the committee of the chess society, 2 years on the committees of the maths society, Unicef on Campus, the physics society, the Liberal Democrats society and one year on the committee of my halls of residence.