**Associate Dean International (Sciences)**

Office: Science III, room 218

Tel +64 3 479 7768

Email florian.beyer@otago.ac.nz

## About

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).

## Teaching responsibilities

My teaching responsibilities include:

- MATH 120 Mathematics fort Scientists
- MATH 304 Partial Differential Equations
- MATH 374 Mathematical Physics
- MATH4DG Differential Geometry
- MATH4MF Mathematical Finance

## Research Interests

### Analysis/PDE

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.*

## Publications

Beyer, F., & Oliynyk, T. (2024). Localized big bang stability for the Einstein-scalar field equations. *Archive for Rational Mechanics & Analysis*, *248*, 3. doi: 10.1007/s00205-023-01939-9
Journal - Research Article

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
Journal - Research Article

Beyer, F., & Ritchie, J. (2022). Asymptotically hyperboloidal initial data sets from a parabolic-hyperbolic formulation of the Einstein vacuum constraints. *Classical & Quantum Gravity*, *39*, 145012. doi: 10.1088/1361-6382/ac79f1
Journal - Research Article

Ames, E., Beyer, F., Isenberg, J., & Oliynyk, T. A. (2022). Stability of asymptotic behaviour within polarized T^{2}-symmetric vacuum solutions with cosmological constant. *Philosophical Transactions of the Royal Society A*, *380*, 20210173. doi: 10.1098/rsta.2021.0173
Journal - Research Article

Ames, E., Beyer, F., Isenberg, J., & Oliynyk, T. A. (2022). Stability of AVTD behavior within the polarized Τ^{2}-symmetric vacuum spacetimes. *Annales Henri Poincaré*, *23*, 2299-2343. doi: 10.1007/s00023-021-01142-0
Journal - Research Article