Current affiliation: Warwick Mathematics Institute, University of Warwick
Funded by:
The Leverhulme Trust

Mathematics Institute
Zeeman Building
University of Warwick
Coventry CV4 7AL

Office: D2.03, Zeeman Building

Phone: +44 (0)24 761 51345
Email: t.hudson.1 (usual symbol)

Career and education
  • 2010 - 2014: DPhil in Mathematics at OxPDE, Mathematical Institute, University of Oxford.
    • Thesis title: Stability and Regularity of Defects in Crystalline Solids.
    • Supervised by Christoph Ortner.
    • Funded by 4-year full studentship.
  • 2006-2010: MMath in Mathematics, Merton College and Mathematical Institute, University of Oxford.
    • Classification: First class.

Professional Memberships and Activities

Principal research interests and expertise

My research focuses on questions relating to the mathematics of solid materials, and principally on crystals. Crystals are made up of atoms laid out in a regular repeating pattern, and include most metals at room temperature and pressure.

I am particularly interested in modelling defects and microstructure of these materials, i.e. the behaviour of small-scale phenomena which affect material properties of crystals on much larger scales. Defects are known to play an important role in the behaviour of plastic (or irreversible) deformation of crystals, and ultimately govern their failure. Deriving and improving predictive models for the evolution of microstructure therefore has important potential consequences for engineering applications.

Some research topics I have worked on in the past include:

  • Micromechanics of materials:
    • Crystalline defects, especially dislocations and their evolution
    • Thermodynamics limits: linking microscopic and macroscopic properties of solids
    • Metastability and temperature-driven evolution of defects
  • Asymptotic methods in the Calculus of Variations, PDE and Stochastic Analysis:
    • Gamma-convergence techniques
    • Stochastic Homogenization
    • Large Deviations Theory


People I have worked with during my career include:

Publications and other media

Publications available online:

Publications in preparation:

  • Thomas Hudson, Mark Peletier and Patrick van Meurs. Atomistic origins of dislocation dynamics at finite temperature.
Doctoral thesis:

  • A digital copy of my doctoral thesis, entitled "Stability and Regularity of Defects in Crystalline Solids", may be found here.

Other media

  • A video of a research presentation I made at the workshop "Analysis of Dislocation Models for Crystal Defects" at the Casa Matemática Oaxaca in June 2017 can be found here.