Louie Bernhardt

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 [dot] unimelb [dot] edu [dot] au

Research interests

I am interested in mathematical general relativity and in partial differential equations more broadly. My research focuses on global properties of solutions to wave equations in general relativity, looking specifically at scattering problems, nonlinear stability problems, and long-time asymptotics. I am also interested in nonlinear wave equations that exhibit finite-time blowup.

Publications

2. Linear waves on the expanding region of Schwarzschild-de Sitter spacetimes: Forward asymptotics and scattering from infinity, published, Comm. Math. Phys. 406(1), (2025).

1. John’s blow up examples and scattering solutions for semi-linear wave equations (with Volker Schlue and Dongxiao Yu), To appear in 2023 MATRIX Annals arXiv:2404.12878.

Talks

6. Scattering of linear waves on the expanding region of Schwarzschild-de Sitter spacetimes, November 2024, Seminar on Mathematical General Relativity at the Laboratoire Jacques-Louis Lions, Sorbonne Université

5. Linear waves on the expanding region of Schwarzschild-de Sitter spacetimes: Forward asymptotics and scattering from infinity, September 2024, Analysis Seminar at the University of Melbourne

4. The Role of Curvature in Geometry, September 2024, Pure Mathematics Seminar at the University of Melbourne

3. Linear waves on the expanding region of Schwarzschild-de Sitter spacetimes: Forward asymptotics and scattering from infinity, July 2024, Topics in General Relativity Seminar at the University of Münster

2. John’s blow up examples and scattering solutions for semi-linear wave equations, April 2024, Analysis Seminar at the University of Melbourne

1. Scattering of linear waves on the expanding region of Schwarzschild-de Sitter spacetimes, September 2023, Hyperbolic PDEs and Nonlinear Evolution Programs at MATRIX

Teaching

(2024) In January I was a teaching assistant(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 1 I was a TA for MATH201: Real Analysis, and in semester 2 I was a TA for COMO101: Computational Modelling for Mathematics at the University of Otago

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