Johnny Nicholson

I am a third year PhD student in Pure Mathematics at University College London and am working under the supervision of Prof. Francis Johnson. Previously, I was at the University of Cambridge where I wrote my Part III essay on Exotic Spheres under the supervision of Oscar Randal-Williams.

For further information, see my CV.

Email: j.k.nicholson(at)

Department of Mathematics
University College London
Gower Street
London, WC1E 6BT

Research Interests

My interests lie in algebraic topology and, more specifically, the application of homological algebra to the homotopy classification of CW-complexes and the stable and unstable classification of manifolds. Recently I have been working on solving cancellation problems over integral group rings and applying these results both to the D2 problem of C. T. C. Wall and to give examples of stably diffeomorphic manifolds in dimensions at least 4 which are not homotopy equivalent.

Publications and Preprints

  1. A cancellation theorem for modules over integral group rings, arXiv:1807.00307 (2018).

  2. On CW-complexes over groups with periodic cohomology, arXiv:1905.12018 (2019).

  3. Connected sum decompositions of high-dimensional manifolds with I. Bokor, D. Crowley, S. Friedl, F. Hebestreit, D. Kasprowski, M. Land, arXiv:1909.02628 (2019).

Conferences and Workshops



2018-19 2017-18

Other Activities

I am a coauthor of the textbook Edexcel A-level Further Mathematics Core Pure Mathematics Book 2 which was published by Pearson in March 2018.

I am a contributor to the material on the website Underground Mathematics, which I worked on during the summer of 2015.