[The University of Edinburgh] o Des Higham

Position:
Professor of Numerical Analysis
School of Mathematics
University of Edinburgh
James Clerk Maxwell Building, The King's Buildings, Edinburgh EH9 3FD Scotland U.K.
Telephone: +44 131 650 6018
E-mail: d.j.higham [at] ed.ac.uk
Campus maps
Travelling to the University of Edinburgh

I'm in the Applied and Computational Mathematics research theme

Some photos from a recent workshop

CV
List of publications with pdfs
MATLAB and R files that accompany various publications

My Google Scholar profile

Some recent publications:
  • Deceptive Diffusion: Generating Synthetic Adversarial Examples, 10th Int. Conf. on Scale Space and Var. Meth. in Comp. Vision, 2025
  • Stealth Edits for Provably Fixing or Attacking Large Language Models, NeurIPS 2024
  • How Adversarial Attacks Can Disrupt Seemingly Stable Accurate Classifiers, Neural Networks, 2024
    • Latest preprints:
  • Embedding Hidden Adversarial Capabilities in Pre-Trained Diffusion Models
  • Rethinking Oversmoothing in Graph Neural Networks: A Rank-Based Perspective
  • Vulnerability Analysis of Transformer-based Optical Character Recognition to Adversarial Attacks
  • Can We Rely on AI?
    • Recent article for Herald newspaper on AI Safety Accessible lectures
    Video of a recent public lecture
    Poster for Curle Lecture at University of St Andrews
    Current and upcoming funded research projects:
  • 2025: A Numerical Analysis Treatment of Adversarial Perturbations in AI, Research Fellowship from The Leverhulme Trust
  • 2026--2030: Numerical Analysis for Stable AI, Advanced Grant from the European Research Council
    • Some other duties/memberships:
    Fellow of the Royal Society of Edinburgh
    Fellow of the Society for Industrial and Applied Mathematics
    On the Editorial Board of the SIAM Journal on Matrix Analysis and Applications
    On the Editorial Board of the IMA Journal of Numerical Analysis
    Member of the INI Newton Gateway to Mathematics Scientific Advisory Panel
    Member of Physical Sciences Panel for the Hong Kong Research Assessment Exercise 2026
    On the Management Committee of the International Centre for Mathematical Sciences
    On the Executive Team of the UK Knowledge Exchange Hub for Mathematical Sciences (KE Hub)
    On the Advisory Board for the Department of Excellence Program at Gran Sasso Science Institute
    Fellow of the Generative AI Lab at the University of Edinburgh
    Senior Research Affiliate in the Centre for Technomoral Futures
    On the Advisory Board for the Doctoral Training Centre on Mathematics of Random Systems
    Member of Engineering and Physical Sciences Research Council (EPSRC) peer review college
    Formerly: Editor in Chief of Society for Industrial and Applied Mathematics (SIAM) Review
    Formerly: Mathematical Sciences panel member for the Research Excellence Framework (REF 2021)
    Formerly: Fellow of the Alan Turing Institute
    Formerly: Member of the Scientific Program Committee for 10th International Congress on Industrial and Applied Mathematics (ICIAM 2023), Tokyo
    Research Interests:
    Numerical Analysis: the design and evaluation of computational methods.
    Main area: Stochastic Computation and its relevance in
    Artificial Intelligence, Machine Learning, Data Analytics, Network Science, Uncertainty Quantification,
    and its application to
    Sociological/Technological Networks, Future Cities/Digital Economy, Computational Biology.
    PhD students supervised/co-supervised
  • Lucas Beerens
  • Aizhan Issagali
  • Alix Leroy
  • Kevin Zhang
    • Some information if you're interested in studying for a PhD in the school
    Books:

    Courses that I have recently been involved with:
    Numercial ODEs and Applications
    Numerical Methods for Data
    Scottish Mathematical Sciences Training Centre
    Here are some old tips on writing. (Here's a pdf version.)
    Connect with Maths:
    Additional material for the graph theory workshop for high school pupils that I coorganised with Heather Yorston
    Data:
    The Strathclyde MUFC Twitter Data Set
    MATLAB and R files:
    Some MATLAB and R files that accompany various publications.
    CONTEST: A Controllable Test Matrix Toolbox for MATLAB
    I'm in:
    Oh look:
    Pictures of places named after MATLAB commands (please send me yours):
    On Saturday mornings I can often be found shuffling round a park.

    Last modified June 2025
    d.j.higham [at] ed.ac.uk