## MATHS

Until January 2016 I was a PhD student in the Department of Mathematics and Statistics at The Open University, working under the supervision of Ian Short. Although my job now lies outside of academia, I am doing my best to keep involved in research. My main research area is in the theory of continued fractions, approached from the viewpoint of hyperbolic geometry. More broadly, I am interested in Diophantine approximation, Kleinian group theory, complex dynamics and other related areas. In the spring of 2015 I spent two months as a visiting researcher at the University of the Witwatersrand, Johannesburg, working alongside Meira Hockman.

**Publications**

- Short, I., Walker, M., 2016. Geodesic Rosen continued fractions.
*The Quarterly Journal of Mathematics*, 67(4), pp. 519-549.*arXiv:1310.1585*. - Short, I., Walker, M., 2016. Even-integer continued fractions and the Farey tree. In:
*Symmetries in maps, graphs and polytopes*, Springer, pp. 297-300.*arXiv:1508.01373*.

Invited talks

Invited talks

- February 2016: Continued fractions and semigroups of Mobius transformations. Dynamical Systems and Analysis seminar, the University of Manchester
- June 2015: Convergence of integer continued fractions. Discrete mathematics seminar, the University of Manchester.
- April 2015: Gaussian integer continued fractions. Mathematics seminar, the University of the Witwatersrand, Johannesburg.
- November 2014: Strong approximation in Fuchsian groups: a geometric approach. Manchester-Birmingham-London-Bristol Groups and Their Applications Triangle Meeting: Groups and Surfaces, Birkbeck, University of London.

**Selected contributed talks**

- August 2015: Gaussian integer continued fractions. Young Researchers in Mathematics Conference, University of Oxford Mathematical Institute.
- June 2015: Continued fractions with coefficients in \(\mathbb{Z}[\sqrt{2}i]\). Summer Postgraduate Student Day, The Open University, Milton Keynes.

- March 2015: Gaussian integer continued fractions, the Picard Group, and hyperbolic geometry. Postgraduate Conference in Complex Dynamics, De Morgan House, London.

- July 2014: Even integer continued fractions: a geometric approach. Young Researchers in Mathematics Conference, University of Warwick.
- July 2013: Rosen's solution to the word problem for the Hecke groups. Postgraduate Group Theory Conference, University of Manchester.

**Posters**

- August 2015: Gaussian integer continued fractions. Heilbronn Institute Poster Competition, Young Researchers in Mathematics Conference, University of Oxford Mathematical Institute.
- March 2014: Paths through the Hecke graphs. SET For Britain poster competition final, House of Commons, London.
- April 2012: Geodesic Rosen continued fractions. Women in Mathematics Day, Centre for Mathematical Sciences, University of Cambridge.

**Grants and prizes**

- August 2015: First Prize in the Heilbronn Institute Poster Competition, Young Researchers in Mathematics Conference, University of Oxford Mathematical Institute.
- November 2014: Grant of 30,000 ZAR from the Centre of Excellence in Mathematical and Statistical Sciences at the University of the Witwatersrand to fund a two month research visit.
- January 2014: Funding for a three month internship at The Brilliant Club as part of the Santander SME Internship Programme.
- November 2013: Grants from the London Mathematical Society, the British Society for the History of Mathematics, the International Commission on the History of Mathematics, and The Open University, totalling £6000, to organise the "24th Novembertagung on the History of Mathematics" conference in London.
- October 2012: Fully funded PhD studentship from The Open University.

**Attended Conferences**

- May 2015: IMSXXV, Celebrating 25 years of low-dimensional dynamics at Stony Brook, Stony Brook University, New York.
- October 2014: Continued Fractions and Geometry of Lattices, University of Liverpool.
- July 2014: Symmetries in Graphs, Maps and Polytopes, West Malvern.
- April 2014: Winter School on Kleinian Groups and Transcendental Dynamics, Universität Bremen.
- June 2013: Young Researchers in Mathematics, University of Edinburgh.
- March 2013: British Mathematical Colloquium, University of Sheffield._

## HISTORY OF MATHS

I completed my master's thesis under supervision of Prof. Jeremy Gray, on the topic of Henri Poincaré's

*Théorie des groups Fuchsiens*and the generalisation of the platonic solids. This led me to spend two months studying the history of mathematics at Aarhus University in Denmark, where I began researching the history of regular maps. More recently I've become interested the relations between history and pedagogy of maths.**Activities**- March 2016: Talk. Creating worlds from nothing: Geometry from Euclid to Poincaré. Princes Teaching Institute History of Mathematics Subject Day, De Morgan House, London.
- June 2015: Conference talk. The history of mathematics as a catalyst for widening participation. IMA International Conference on Barriers and Enablers to Learning Maths, University of Glasgow.
- October 2014: Conference review. BSHM Research in Progress.
*BSHM Bulletin*, 29(3), pp. 210-211. - July 2014: Attended conference. 7th European Summer University on the History and Epistemology in Mathematics Education, Aarhus University, Copenhagen.
- November 2013: Organised conference. The 24th Novembertagung on the History of Mathematics, De Morgan House, London.

- March 2013: Conference talk. Henry Roy Brahana and the classification of regular maps. BSHM Research in Progress, The Queen's College, University of Oxford.

- November 2012: Conference talk. The changing perceptions of Henry Roy Brahana's work on the classification of regular maps. The 23rd Novembertagung on the History of Mathematics, Bergische Universität Wuppertal.
- March 2012: Conference talk. Poincaré's constructions of Riemann surfaces. BSHM Research in Progress, The Queen's College, University of Oxford.

## LINKS

Some of my favourites...

**Mathematicians**- Super supervisor - Ian Short.
- Top office mate and complex dynamicist - David Martí Pete.
- Doctoral brother - Matthew Jacques.

- Great group theorist - Nick Gill.
- Logician and public engager - Katie Chicot

**Mathematics**- Preprints central - The arXiv.
- Reviews, abstracts and BibTeX info - MathSciNet.
- Magazine articles about maths - Plus Magazine.
- Free program for drawing vector graphics - Inkscape.

*Three Möbius maps walk into a pub: an elliptic, a parabolic and a loxodromic. They go to the bar and ask for three beers, but the bartender says "Sorry, but I can't serve you without Id."*

(courtesy of Matthew Jacques)