Elliot Marshall

Research Interests

General Relativity, Partial Differential Equations, Numerical Methods, Analysis. My current work uses a combination of analytical and numerical methods to study the global stability properties of cosmological perfect fluid models in Einstein's general theory of relativity.

Preprints and Publications

1. (with Grigorios Fournodavlos and Todd Oliynyk) Future Stability of Tilted Two-Fluid Bianchi I Spacetimes, arXiv:2508.15155

2. Instability of Slowly Expanding FLRW Spacetimes, Class. Quantum Grav. 42, (2025), 105005, pdf

3. (with Florian Beyer and Todd Oliynyk) Past instability of FLRW solutions of the Einstein-Euler-scalar field equations for linear equations of state p=Kρ with 0 ≤ K < 1/3, Phys. Rev. D 110, (2024), 044060, pdf

4. (with Grigorios Fournodavlos and Todd Oliynyk) Future stability of perfect fluids with extreme tilt and linear equation of state p=c_{s}^{2}ρ for the Einstein-Euler system with positive cosmological constant: The range 1/3 < c_{s}^{2} < 3/7, arXiv:2404.06789

5. (with Florian Beyer and Todd Oliynyk) Future instability of FLRW fluid solutions for linear equations of state p=Kρ with 1/3 < K < 1, Phys. Rev. D 107, (2023), 104030, pdf

6. (with Todd Oliynyk) On the stability of relativistic perfect fluids with linear equations of state p=Kρ where 1/3 < K < 1, Lett. Math. Phys. 113 (2023), 102, pdf

Education

• PhD in Mathematics (2022 - Present), Monash University, Main Supervisor: Todd Oliynyk, External Co-Supervisor: Florian Beyer

• BSc (Hons), 1st Class in Mathematics (2021), University of Otago, Supervisor: Jörg Frauendiener

• BSc in Mathematics (2020), University of Otago.

Past and Upcoming Talks

• Harvard CMSA General Relativity Seminar, 25 March 2025.

• Joint Meeting of the NZMS, AustMS, and AMS, University of Auckland, 9-13 December, 2024.

• Problems and Progress in Dispersive PDE, University of Otago, 5-6 December, 2024.

• 12th Australasian Conference on General Relativity and Gravitation (ACGRG), Hobart, Tasmania, November 27 - December 1, 2023.

• MATRIX conference on Hyperbolic PDEs and Non-Linear Evolution Problems, Creswick, Australia, September 18-29, 2023.

• Australia-New Zealand Student Conference on Relativity, Cosmology, and Astrophysics (Online), May 8-10, 2023.

• Interdisciplinary junior scientist workshop: Mathematical General Relativity, Wildberg, Germany, February 26 - March 10, 2023.

Professional Activities

• I was the main organiser of the first Australia-New Zealand Student Conference on Relativity, Cosmology, and Astrophysics, May 8-10, 2023.