Kia ora! I am a 4th year PhD student in the School of Mathematics and Statistics at the University of Melbourne. My supervisor is Volker Schlue.
A copy of my CV can be found here.
My email is lbernhardt[at]student.unimelb.edu.au
I am interested in mathematical general relativity and in partial differential equations more broadly. My research focuses on global properties of solutions to hyperbolic differential equations in general relativity, looking specifically at stability problems, scattering problems, and long-time asymptotics. I am also interested in nonlinear wave equations that exhibit finite-time blowup.
3. Future stability of solutions of the Einstein-nonlinear scalar field system with decelerated expansion, (2025) (view preprint at arXiv:2508.15303).
2. Linear waves on the expanding region of Schwarzschild-de Sitter spacetimes: Forward asymptotics and scattering from infinity, Comm. Math. Phys. 406(1), (2025).
1. (with Volker Schlue and Dongxiao Yu) John’s blow up examples and scattering solutions for semi-linear wave equations, 2023 MATRIX Annals, MATRIX Book Series, vol 6. Springer, (2025).
13. Stability of cosmological spacetimes undergoing decelerated expansion (Upcoming), Harmonic Analysis and Hamiltonian PDE Session, AustMS Annual Conference 2025, La Trobe University, Australia
12. Stability of cosmological spacetimes undergoing decelerated expansion (Upcoming), Seminar, Differential geometry and general relativity, KTH, Sweden
11. Stability of cosmological spacetimes undergoing decelerated expansion (Upcoming), General Relativity Reading Group, University of Cambridge, UK
10. Stability of cosmological spacetimes undergoing decelerated expansion (Nov 2025), Junior Analysis Seminar, Imperial College London, UK
9. Stability of cosmological spacetimes undergoing decelerated expansion (Nov 2025), Cretan Stars Workshop in Anogia, Greece
8. Future stability of decelerated FLRW solutions to the Einstein equations (Sep 2025), Analysis, Geometry and PDE seminar, University of Monash, Australia
7. Scattering of linear waves on the expanding region of Schwarzschild-de Sitter spacetimes (Dec 2024), Joint Meeting of the NZMS, AustMS, and AMS, University of Auckland, New Zealand
6. Scattering of linear waves on the expanding region of Schwarzschild-de Sitter spacetimes (Nov 2024), Seminar on Mathematical General Relativity, Sorbonne Université, France
5. Linear waves on the expanding region of Schwarzschild-de Sitter spacetimes: Forward asymptotics and scattering from infinity (Sep 2024), Analysis Seminar, University of Melbourne, Australia
4. The Role of Curvature in Geometry (Sep 2024), Pure Mathematics Seminar, University of Melbourne, Australia
3. Linear waves on the expanding region of Schwarzschild-de Sitter spacetimes: Forward asymptotics and scattering from infinity (Jul 2024) Topics in General Relativity Seminar, University of Münster, Germany
2. John’s blow up examples and scattering solutions for semi-linear wave equations (Apr 2024), Analysis Seminar, University of Melbourne, Australia
1. Scattering of linear waves on the expanding region of Schwarzschild-de Sitter spacetimes (Sep 2023), Hyperbolic PDEs and Nonlinear Evolution Problems, MATRIX, Australia
(2025) In semester 2 I was a teaching assistant (TA) for MAST20026: Real Analysis, while in semester 1 I was a TA for MAST20033: Real Analysis Advanced and MAST90012: Measure Theory, all at the University of Melbourne.
(2024) In January I was a TA for the class General Relativity at the AMSI Summer School in the Mathematical Sciences at the Australian National University.
(2023) In semester 1 I was a TA for MAST20026: Real Analysis, MAST10021: Advanced Calculus, and MAST10006: Calculus 2 at the University of Melbourne.
(2021) In semester 2 I was a TA for COMO101: Computational Modelling for Mathematics , and in semester 1 I was a TA for MATH201: Real Analysis at the University of Otago.