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

  • Sept 2019 - Present: Assistant Professor at the Mathematics Institute, University of Warwick.
  • 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


In the academic year 2019 - 2020, I am leading MA134 Geometry and Motion and guest lecturing for PX914 Predictive Modelling and Uncertainty Quantification (part of the training programme of the HetSys Centre for Doctoral Training).

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.

A more recent topic I have begun working on is the theory of coarse-graining for dynamical systems, particular those used in molecular simulation techniques. Coarse-graining techniques attempt to reduce complex mathematical models to simpler ones for practical computational reasons. One approach to performing this reduction is based on the Mori-Zwanzig formalism, which uses project operators to inspire data-driven numerical approximation techniques.

Some keywords which describe various 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
  • Coarse-graining for dynamical systems
    • The Mori-Zwanzig formalism


People I have worked with during my career include:

Publications and other media

Publications available online:

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 "Mathematical design of new materials - strategies and algorithms for the design of alloys and metamaterials" at the ICMS in March 2019 can be found here.
  • 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.