Elliot Marshall

Research Interests

General Relativity, Numerical Methods, Partial Differential Equations, Analysis. I am interested in using both numerical methods and analysis to investigate problems in mathematical relativity, such as non-linear stability and shock formation, with a particular focus on cosmology. 

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 - 2025), 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

• Cretan Stars Workshop, Anogia, Crete, 1-3 November 2025

• 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.

• 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.