Research Interests

I am a mathematical and numerical relativist specialising in global properties of space-times and solving Einstein's equations on the computer in a variety of different contexts.

Mathematical general relativity ties fundamental problems of gravitational physics with beautiful questions in mathematics. The object is the study of manifolds equipped with a Lorentzian metric satisfying the Einstein field equations. Due to the broad scope of questions one can ask about the physics, many different areas of mathematics are employed such as group theory, topology, differential geometry and partial differential equations.

Numerical relativity is used to obtain approximations to the complicated systems produced by the Einstein equations. In general these systems will have no closed form solutions and thus numerical methods must be employed. Differential geometry, PDE theory and numerical methods work together to simulate complicated space-times such as binary black hole or neutron star mergers. High performance computing facilities are utilised and hundreds if not thousands of CPU cores are required to complete simulations in reasonable time frames.

I have many Honours, Masters and PhD projects available in these areas, the details of which are on my website: https://www.chrisdoesmaths.com

I am also interested in applying mathematics, algorithm development and scientific programming to real world problems. This is accomplished together with a colleague from the University of Otago through our company SCRI: https://www.scri.co.nz