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.
Future stability of solutions of the Einstein-nonlinear scalar field system with decelerated expansion, (2025) (view preprint at arXiv:2508.15303).
Linear waves on the expanding region of Schwarzschild-de Sitter spacetimes: Forward asymptotics and scattering from infinity, Comm. Math. Phys. 406(1), (2025).
(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).
PhD completion seminar, University of Melbourne, Australia (Feb. 2026)
Harmonic Analysis and Hamiltonian PDE Session, AustMS Annual Conference 2025, La Trobe University, Australia (Dec. 2025)
Seminar, Differential geometry and general relativity, KTH, Sweden (Dec. 2025)
General Relativity Reading Group, University of Cambridge, UK (Nov. 2025)
Junior Analysis Seminar, Imperial College London, UK (Nov. 2025)
Cretan Stars Workshop in Anogia, Greece (Nov. 2025)
Analysis, Geometry and PDE seminar, University of Monash, Australia (Sep. 2025)
Joint Meeting of the NZMS, AustMS, and AMS, University of Auckland, New Zealand (Dec. 2024)
Seminar on Mathematical General Relativity, Sorbonne Université, France (Nov. 2024)
Analysis Seminar, University of Melbourne, Australia (Sep. 2024)
Pure Mathematics Seminar, University of Melbourne, Australia (Sep. 2024)
Topics in General Relativity Seminar, University of Münster, Germany (Jul. 2024)
Analysis Seminar, University of Melbourne, Australia (Apr. 2024)
Hyperbolic PDEs and Nonlinear Evolution Problems, MATRIX, Australia, (Sep. 2023)
Australia–New Zealand Student Conference on Relativity, Online, (May. 2023)
I am/was a class tutor for the following subjects at the University of Melbourne:
(2026) MAST20033: Real Analysis Advanced, MAST90020: Functional Analysis,
(2025) MAST20026: Real Analysis, MAST20033: Real Analysis Advanced, MAST90012: Measure Theory,
(2023) MAST10006: Calculus 2, MAST10021: Advanced Calculus, MAST20026: Real Analysis.
In 2024, I was a class tutor for the General Relativity subject at the AMSI Summer School in the Mathematical Sciences, ANU.
I was a class tutor for the following subjects at the University of Otago:
(2021) COMO101: Computational Modelling for Mathematics, MATH201: Real Analysis,
(2020) MATH201: Real Analysis.