Career

  • 2016 - date: PhD student, DAMTP, CCA, University of Cambridge. 
  • 2015 - 2016: M.Math. (Part III), University of Cambridge.
  • 2012 - 2015: B.A. Maths, University of Cambridge.

Research

I am a member of the Applied Functional and Harmonic Analysis group within the Cambridge Centre for Analysis at DAMTP. My current interests are:

  • Spectral theory and the existence (or non-existence) of algorithms to solve computational problems in infinite dimensions.
  • The Solvability Complexity Index Hierarchy. I am one of the main contributors to the development of the SCI hierarchy, a classification of the difficulty of numerical problems.
  • Recent results show neural networks are in general unstable. This is not just a problem in image classification but also in image denoising and reconstruction (where stable methods already exist), and is attracting an increasing amount of interest/awareness. Part of my PhD seeks to fix this in the context of noisy subsampling.
  • Spectral/pseudospectral methods and linear algbra in infinite dimensions.
  • Scattering problems and other problems related to computational fluid mechanics.

Selected Publications

For a list of publications as well as more detail on my research, see: http://www.damtp.cam.ac.uk/user/mjc249/home.html