{ padding-top: 0px; }

Matthew Colbrook

You have reached the webpage of Matthew Colbrook, a Junior Research Fellow at Trinity College, Cambridge (UK). Here you can find info on things like interests, publications and contact details. I am always keen to work with new people so please get in touch. My CV can be found here (last updated 29th Oct 2020).

Research Interests

Broadly speaking, I am interested in mathematical and computational/numerical analysis. My work particularly concerns the existence and development of algorithms related to spectral theory, solutions of PDEs, neural networks and inverse problems/optimisation.

More specifically:

  • Spectral theory and the existence (or non-existence) of algorithms to solve computational problems in infinite dimensions. Infinite dimensional spectral problems are notoriously difficult. Part of my thesis concerned the development of a new resolvent based family of algorithms to tackle these problems.
  • 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. Part of my thesis concerned the extension of this hierarchy and developing new techniques to study it.
  • The quest for stability in deep learning and neural networks. 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. I seek to fix this in the context of noisy subsampling.
  • Spectral/pseudospectral methods and linear algebra in infinite dimensions.
  • Scattering problems and other problems related to computational fluid mechanics.

Main Academic Awards

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

IMA Lighthill-Thwaites Prize Finalist 2019
Biannual international prize given by IMA to top early career (Ph.D./postdoc) applied mathematicians.
(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).

Cambridge-Imperial Computational PhD Seminar

Introducing the Cambridge-Imperial Computational PhD Seminar Series. This will occur twice per term featuring a host of student talks and guest plenary speakers. Details can be found here. If you want to give a talk, please get in touch! Update: currently postponed until further notice due to covid-19.

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