I am an applied mathematician working on problems in analysis, PDEs and geometry many of which are motivated by mathematical physics, especially general relativity and cosmology. I am a member of the Gravity group of the University of Otago.
Since November 2022, I am the Associate Dean International (Sciences).
My teaching responsibilities include:
- MATH 120 Mathematics fort Scientists
- MATH 304 Partial Differential Equations
- MATH 374 Mathematical Physics
- MATH4DG Differential Geometry
- MATH4MF Mathematical Finance
My research is about asymptotics and singular limits of solutions to partial differential equations (PDEs), especially so-called Fuchsian PDEs. These are nonlinear systems of wave equations appearing frequently in mathematics and mathematical physics where some of the coefficients may have characteristic “1/t-singularities”.
The main concerns of my research are, (i), global existence, stability and asymptotics of solutions of the Cauchy problem evolved towards the singular time t=0 from some initial time T>0, and, (ii), singular initial value problems where one seeks solutions that are launched from the singular time t=0 into the increasing time direction.
Mathematical/computational general relativity/cosmology
I am interested in fundamental questions, like nonlinear stability of cosmological models, Roger Penrose's cosmic censorship conjecture, asymptotic simplicity and Mixmaster dynamics.