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.
Beyer, F., Marshall, E., & Oliynyk, T. A. (2023). Future instability of FLRW fluid solutions for linear equations of state p = Kp with 1/3 < K < 1. Physical Review D, 107, 104030. doi: 10.1103/PhysRevD.107.104030
Beyer, F., & Ritchie, J. (2022). Asymptotically hyperboloidal initial data sets from a parabolic-hyperbolic formulation of the Einstein vacuum constraints. Classical & Quantum Gravity. Advance online publication. doi: 10.1088/1361-6382/ac79f1
Ames, E., Beyer, F., Isenberg, J., & Oliynyk, T. A. (2022). Stability of asymptotic behaviour within polarized T2-symmetric vacuum solutions with cosmological constant. Philosophical Transactions of the Royal Society A, 380, 20210173. doi: 10.1098/rsta.2021.0173
Ames, E., Beyer, F., Isenberg, J., & Oliynyk, T. A. (2022). Stability of AVTD behavior within the polarized Τ2-symmetric vacuum spacetimes. Annales Henri Poincaré, 23, 2299-2343. doi: 10.1007/s00023-021-01142-0
Beyer, F., & LeFloch, P. G. (2021). A numerical algorithm for Fuchsian equations and fluid flows on cosmological spacetimes. Journal of Computational Physics, 431, 110145. doi: 10.1016/j.jcp.2021.110145