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Matthew Colbrook

You have reached the webpage of Matthew Colbrook, a Junior Research Fellow at Trinity College, Cambridge (UK). I completed my PhD, "The Foundations of Infinite-Dimensional Spectral Computations", in September 2020 at the University of Cambridge. For the acadmic year 2021-2022 I will be visiting École Normale Supérieure's Centre Sciences des Données under a Fondation Sciences Mathématiques de Paris Fellowship.

Research Interests

My work concerns the development of algorithms related to spectral theory, solutions of PDEs, neural networks, compressed sensing and inverse problems/optimisation. More specifically:

  • Spectral computational problems in infinite dimensions
  • Stability and accuracy in deep learning
  • The Solvability Complexity Index Hierarchy and foundations of computational mathematics
  • Infinite-dimensional numerical linear algebra
  • Spectral and pseudospectral methods for PDEs
  • Scattering problems, acoustics, and other problems related to computational fluid mechanics

Main Academic Awards

IMA Lighthill-Thwaites Prize 2021 (+ Finalist in 2019)
Biannual international prize given by IMA to top early career applied mathematicians.
(see here for details).

Cecil King Travel Scholarship 2020
Annual prize of the London Mathematical Society given "to a young mathematician of outstanding promise".
(see here for details).

Smith-Knight/Rayleigh-Knight Prize 2018
Grade I (top grade). Best first-year graduate piece of work in Mathematics Department of University of Cambridge.
(see here for details).

Mayhew Prize 2016
Best masters degree in Department of Applied Mathematics and Theoretical Physics, University of Cambridge.
(see here for details).

Caltech SURF Scholarship 2015
(see here for details).

Contact Details

Email: m[dot]colbrook[at]damtp.cam.ac.uk

Address: Department of Applied Mathematics and Theoretical Physics (DAMTP), University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK