Areas of Expertise

  • Nonlinear partial differential equations
  • Singular limits of elliptic and parabolic systems
  • Reaction-diffusion-convection systems and travelling waves
  • Applications of PDE to biology
  • Geometric methods for image processing

Publications

  1. & Compensated Convexity Methods for Approximations and Interpolations of Sampled Functions in Euclidean Spaces: Theoretical Foundations. SIAM Journal on Mathematical Analysis 48(6), 4126-4154.
  2. & Self-similar fast-reaction limits for reaction–diffusion systems on unbounded domains. Journal of Differential Equations 261(3), 2210-2250.
  3. & Lack of symmetry in linear determinacy due to convective effects in reaction-diffusion-convection problems. Tamkang Journal of Mathematics 47(1), 51-70.
  4. & Compensated convexity, multiscale medial axis maps and sharp regularity of the squared distance function. SIAM Journal on Mathematical Analysis 47(6), 4289-4331.
  5. & Compensated convexity and Hausdorff stable extraction of intersections for smooth manifolds. Mathematical Models and Methods in Applied Sciences 25(5), 839-873.

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Teaching

  • MA-142 Classical Mechanics (of Particles)

    An introduction to the concepts and principles of classical mechanics. The course covers the use of vectors to model physical problems and various quantities from physics. It then introduces Newton¿s laws of motion and considers some of the fundamental examples such as rocket motion and planetary motion.

  • MA-231 Advanced Geometry

    This module covers conics sections, projective geometry as well as problems in non-euclidean geometry.

  • MA-E01 Year in Industry or Abroad

    Students are required to take appropriate work or select appropriate maths modules. The modules chosen are detailed within a Learning Agreement which must be approved by the Study Abroad Co-ordinator at Swansea University before the student leaves Swansea.

  • MA-R01 Year in Industry or Abroad

    Students are required to take appropriate work or select appropriate maths modules. The modules chosen are detailed within a Learning Agreement which must be approved by the Study Abroad Co-ordinator at Swansea University before the student leaves Swansea.

Supervision

  • Untitled (current)

    Student name:
    PhD
    Other supervisor: Prof Niels Jacob
  • Individual variability in dispersal and invasion speed (current)

    Student name:
    PhD
    Other supervisor: Prof Luca Borger
  • Untitled (current)

    Student name:
    PhD
    Other supervisor: Dr Carlo Mercuri