I am a research visitor in the Geometry and Topology Group within the School of Mathematics at The University of Manchester.

My main area of research is algebraic topology, and my PhD thesis is concerned with the integral cohomology ring of the symmetric square of quaternionic projective space. I am also becoming interested in applied algebraic topology.

The main results of my PhD thesis form part of the preprint that has appeared on arXiv.

I have extended my results to the general case of even spaces; these have torsion free integral cohomology, concentrated in even dimensions.

Our ongoing project includes the cases of the octonionic projective plane, the octonionic flag manifold, and certain weighted projective spaces.

Boote, Y. and Ray, N.(2018) On the symmetric squares of complex and quaternionic projective space. *Glasgow Mathematical Journal* [First published online 13 February 2018] DOI: 10.1017/S0017089518000034

- Some aspects of symmetric products , British Mathematical Colloquium 2017, April, Durham, England.

- Configuration spaces, the octonionic projective plane, and the potential applications , 7th Applied Algebraic Topology Meeting, September 2016, Durham, England.

- Configuration spaces, compactifications, and weighted projective space , 31st British Topology Meeting, August 2016, Glasgow, Scotland.

- Symmetric squares of even spaces , Transpennine Topology Triangle 99, July 2016, Sheffield, England.

I believe that the ideas and concepts of mathematics should be shared and celebrated with everyone, including students who have learning disabilities.

My vision is supported by many, in particular, Dr Rosa Archer, the team leader of PGCE secondary mathematics at the Manchester Institute of Education, and Paul Cronin, the Head teacher of Redbridge High School in Liverpool. These two have helped make my outreach programme 2015/16 possible.