Florian Beyer, Our people, Department of Mathematics and Statistics

(PhD Potsdam)

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., Marshall, E., & Oliynyk, T. A. (2024). Past instability of FLRW solutions of the Einstein-Euler-scalar field equations for linear equations of state p=Kρ with 0≤K<1/3. Physical Review D, 110, 044060. doi: 10.1103/PhysRevD.110.044060 Journal - Research Article

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 T²-symmetric vacuum solutions with cosmological constant. Philosophical Transactions of the Royal Society A, 380, 20210173. doi: 10.1098/rsta.2021.0173 Journal - Research Article

2024

Journal - Research Article

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

2023

Journal - Research Article

2022

Journal - Research Article

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

2021

Journal - Research Article

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

Beyer, F., Oliynyk, T. A., & Olvera-Santamaría, J. A. (2021). The Fuchsian approach to global existence for hyperbolic equations. Communications in Partial Differential Equations, 46(5), 864-934. doi: 10.1080/03605302.2020.1857402

2020

Journal - Research Article

Beyer, F., Frauendiener, J., & Hennig, J. (2020). Explorations of the infinite regions of spacetime. International Journal of Modern Physics D, 29(10), 2030007. doi: 10.1142/S0218271820300074

Beyer, F., Frauendiener, J., & Ritchie, J. (2020). Asymptotically flat vacuum initial data sets from a modified parabolic-hyperbolic formulation of the Einstein vacuum constraint equations. Physical Review D, 101, 084013. doi: 10.1103/PhysRevD.101.084013

2019

Journal - Research Article

Ames, E., Beyer, F., & Isenberg, J. (2019). Contracting asymptotics of the linearized lapse-scalar field sub-system of the Einstein-scalar field equations. Journal of Mathematical Physics, 60, 102504. doi: 10.1063/1.5115104

Beyer, F., Escobar, L., Frauendiener, J., & Ritchie, J. (2019). Numerical construction of initial data sets of binary black hole type using a parabolic-hyperbolic formulation of the vacuum constraint equations. Classical & Quantum Gravity, 36(17), 175005. doi: 10.1088/1361-6382/ab3482

Working Paper; Discussion Paper; Technical Report

Beyer, F., Oliynyk, T. A., & Olvera-Santamaría, J. A. (2019). The Fuchsian approach to global existence for hyperbolic equations. arXiv. Retrieved from https://arxiv.org/abs/1907.04071

Ames, E., Beyer, F., & Isenberg, J. (2019). Contracting asymptotics of the lapse-scalar field sub-system of the Einstein-scalar field equations. arXiv. Retrieved from https://arxiv.org/abs/1904.02854

Other Research Output

Beyer, F. (2019, May). Taming the beast of the cosmological big bang singularity: Dynamics and degrees of freedom. Mathematics Seminar Series, Department of Mathematics & Statistics, University of Otago, Dunedin, New Zealand. [Department Seminar].

2018

Journal - Research Article

Beyer, F., & Paetz, T.-T. (2018). Analysis of a Bianchi-like equation satisfied by the Mars-Simon tensor. Journal of Mathematical Physics, 59, 022501. doi: 10.1063/1.4996700

2017

Journal - Research Article

Beyer, F., Frauendiener, J., Stevens, C., & Whale, B. (2017). Numerical initial boundary value problem for the generalized conformal field equations. Physical Review D, 96(8), 084020. doi: 10.1103/PhysRevD.96.084020

Beyer, F., Escobar, L., & Frauendiener, J. (2017). Asymptotics of solutions of a hyperbolic formulation of the constraint equations. Classical & Quantum Gravity, 34(20), 205014. doi: 10.1088/1361-6382/aa8be6

Ames, E., Beyer, F., Isenberg, J., & LeFloch, P. G. (2017). A class of solutions to the Einstein equations with AVTD behavior in generalized wave gauges. Journal of Geometry & Physics, 121, 42-71. doi: 10.1016/j.geomphys.2017.06.005

Beyer, F., & LeFloch, P. G. (2017). Self–gravitating fluid flows with Gowdy symmetry near cosmological singularities. Communications in Partial Differential Equations, 42(8), 1199-1248. doi: 10.1080/03605302.2017.1345938

Beyer, F., Escobar, L., & Frauendiener, J. (2017). Criticality of inhomogeneous Nariai-like cosmological models. Physical Review D, 95(8), 084030. doi: 10.1103/PhysRevD.95.084030

Working Paper; Discussion Paper; Technical Report

Beyer, F., & Paetz, T.-T. (2017). Analysis of a Bianchi-like equation satisfied by the Mars-Simon tensor. arXiv. Retrieved from https://arxiv.org/abs/1707.05201

Beyer, F., Escobar, L., & Frauendiener, J. (2017). Criticality of inhomogeneous Nariai-like cosmological models. arXiv. Retrieved from https://arxiv.org/abs/1702.02694

2016

Journal - Research Article

Beyer, F., Escobar, L., & Frauendiener, J. (2016). Numerical solutions of Einstein's equations for cosmological spacetimes with spatial topology S³ and symmetry group U(1). Physical Review D, 93, 043009. doi: 10.1103/PhysRevD.93.043009

2015

Journal - Research Article

Beyer, F., Daszuta, B., & Frauendiener, J. (2015). A spectral method for half-integer spin fields based on spin-weighted spherical harmonics. Classical & Quantum Gravity, 32(17), 175013. doi: 10.1088/0264-9381/32/17/175013

Conference Contribution - Published proceedings: Abstract

Beyer, F., & LeFloch, P. G. (2015). "Matter does not matter" for self-gravitating perfect fluids? [Extended abstract]. Proceedings of the Mathematisches Forschungsinstitut Oberwolfach Workshop: Mathematical Aspects of General Relativity [Report No. 33/2015]. 12(3), (pp. 1867-1935). Zürich, Switzerland: European Mathematical Society. doi: 10.4171/OWR/2015/33

Working Paper; Discussion Paper; Technical Report

Ames, E., Beyer, F., Isenberg, J., & LeFloch, P. G. (2015). A class of solutions to the Einstein equations with AVTD behavior in generalized wave gauges. arXiv. Retrieved from http://arxiv.org/abs/1602.03018

Beyer, F., & LeFloch, P. G. (2015). Dynamics of self-gravitating fluids in Gowdy-symmetric spacetimes near cosmological singularities. arXiv. Retrieved from http://arxiv.org/abs/1512.07187

Beyer, F., Escobar, L., & Frauendiener, J. (2015). Numerical solutions of Einstein's equations for cosmological spacetimes with spatial topology S³ and symmetry group U(1). arXiv. Retrieved from http://arxiv.org/abs/1505.05920v1

2014

Journal - Research Article

Beyer, F., & Hennig, J. (2014). An exact smooth Gowdy-symmetric generalized Taub–NUT solution. Classical & Quantum Gravity, 31(9), 095010. doi: 10.1088/0264-9381/31/9/095010

Beyer, F., Daszuta, B., Frauendiener, J., & Whale, B. (2014). Numerical evolutions of fields on the 2-sphere using a spectral method based on spin-weighted spherical harmonics. Classical & Quantum Gravity, 31, 075019. doi: 10.1088/0264-9381/31/7/075019

Journal - Professional & Other Non-Research Articles

Beyer, F. (2014). General relativity and PDEs [Invited article]. NZMS Newsletter, (122), 7-8.

Conference Contribution - Published proceedings: Full paper

Beyer, F., Doulis, G., Frauendiener, J., & Whale, B. (2014). The spin-2 equation on Minkowski background. In A. Garcia-Parrado, F. C. Mena, R. Moura & E. Vas (Eds.), Progress in Mathematical Relativity, Gravitation and Cosmology (Vol. 60). (pp. 465-468). Berlin: Springer. doi: 10.1007/978-3-642-40157-2_71

Beyer, F., Doulis, G., Frauendiener, J., & Whale, B. (2014). Linearized gravitational waves near space-like and null infinity. In A. Garcia-Parrado, F. C. Mena, R. Moura & E. Vas (Eds.), Progress in Mathematical Relativity, Gravitation and Cosmology (Vol. 60). (pp. 3-17). Berlin: Springer. doi: 10.1007/978-3-642-40157-2_1

Conference Contribution - Published proceedings: Abstract

Beyer, F. (2014). AVTD solutions of Einstein's field equations. Proceedings of the 8th Australia and New Zealand Mathematics Convention (AustMS and NZMS). (pp. 97). Retrieved from http://www.austms2014.ms.unimelb.edu.au/

2013

Journal - Research Article

Beyer, F., & Escobar, L. (2013). Graceful exit from inflation for minimally coupled Bianchi A scalar field models. Classical & Quantum Gravity, 30, 195020. doi: 10.1088/0264-9381/30/19/195020

Ames, E., Beyer, F., Isenberg, J., & LeFloch, P. G. (2013). Quasilinear hyperbolic Fuchsian systems and AVTD behavior in T²-symmetric vacuum spacetimes. Annales Henri Poincaré, 14(6), 1445-1523. doi: 10.1007/s00023-012-0228-2

Journal - Research Other

Blakie, P. B., & Beyer, F. (2013). Table-top cosmology with Bose-Einstein condensates. Annalen der Physik, 525(10-11), A163-A164. doi: 10.1002/andp.201300741

Conference Contribution - Published proceedings: Full paper

Ames, E., Beyer, F., Isenberg, J., & LeFloch, P. G. (2013). Quasilinear symmetric hyperbolic Fuchsian systems in several space dimensions. Contemporary Mathematics, 591, (pp. 25-43). doi: 10.1090/comm/591/11824

Conference Contribution - Published proceedings: Abstract

Ames, E., Isenberg, J., & Beyer, F. (2013). What is the singular behavior of the gravitational field near generic big-bang type events? Proceedings of the Annual Meeting of the Four Corners Section of the APS: Bulletin of the American Physical Society. 58(12). Retrieved from http://meetings.aps.org/Meeting/4CF13/Session/D2.6

2012

Journal - Research Article

Beyer, F., Doulis, G., Frauendiener, J., & Whale, B. (2012). Numerical space-times near space-like and null infinity: The spin-2 system on Minkowski space. Classical & Quantum Gravity, 29(24), 245013. doi: 10.1088/0264-9381/29/24/245013

Beyer, F., & Hennig, J. (2012). Smooth Gowdy-symmetric generalized Taub–NUT solutions. Classical & Quantum Gravity, 29, 245017. doi: 10.1088/0264-9381/29/24/245017

Conference Contribution - Published proceedings: Full paper

Beyer, F. (2012). The cosmic no-hair conjecture: A study of the Nariai solutions. In T. Damour & R. T. Jantzen (Eds.), Proceedings of the Twelfth Marcel Grossman Meeting: On Recent Developments in Theoretical and Experimental General Relativity, Astrophysics and Relativistic Field Theories. (pp. 759-761). Singapore: World Scientific. [Full Paper]

Conference Contribution - Published proceedings: Abstract

Beyer, F. (2012). Guided tour through AVTD regions of the BKL world. Proceedings of the Sixth Australasian Conference on General Relativity and Gravitation. Retrieved from http://www.maths.otago.ac.nz/acgrg6/

Conference Contribution - Verbal presentation and other Conference outputs

Beyer, F. (2012, December). AVTD solutions of Einstein's field equations. Verbal presentation at the New Zealand Mathematical Society Colloquium, Palmerston North, New Zealand.

Beyer, F. (2012, February). Guided tour through AVTD regions of the BKL world. Plenary presentation at the Sixth Australasian Conference on General Relativity and Gravitation, Queenstown, New Zealand.

2011

Journal - Research Article

Beyer, F., & LeFloch, P. G. (2011). Second-order hyperbolic Fuchsian systems: Asymptotic behavior of geodesics in Gowdy spacetimes. Physical Review D, 84, 084036. doi: 10.1103/PhysRevD.84.084036

2010

Journal - Research Article

Beyer, F., & LeFloch, P. G. (2010). Second-order hyperbolic Fuchsian systems and applications. Classical & Quantum Gravity, 27(24), 245012. doi: 10.1088/0264-9381/27/24/245012

2009

Journal - Research Article

Beyer, F. (2009). A spectral solver for evolution problems with spatial S³-topology. Journal of Computational Physics, 228, 6496-6513. doi: 10.1016/j.jcp.2009.05.037

Beyer, F. (2009). Non-genericity of the Nariai solutions: II. Investigations within the Gowdy class. Classical & Quantum Gravity, 26, 235016. doi: 10.1088/0264-9381/26/23/235016

Beyer, F. (2009). Non-genericity of the Nariai solutions: I. Asymptotics and spatially homogeneous perturbations. Classical & Quantum Gravity, 26, 235015. doi: 10.1088/0264-9381/26/23/235015

2008

Journal - Research Article

Beyer, F. (2008). Investigations of solutions of Einstein’s field equations close to λ-Taub–NUT. Classical & Quantum Gravity, 25, 235005. doi: 10.1088/0264-9381/25/23/235005

2006

Journal - Research Article

Schnetter, E., Krishnan, B., & Beyer, F. (2006). Introduction to dynamical horizons in numerical relativity. Physical Review D, 74, 024028. doi: 10.1103/PhysRevD.74.024028

2004

Journal - Research Article

Bishop, N. T., Beyer, F., & Koppitz, M. (2004). Black hole initial data from a nonconformal decomposition. Physical Review D, 69, 064010. doi: 10.1103/PhysRevD.69.064010