My research lies at the intersection of general relativity, differential geometry and hyperbolic PDEs. I am very interested in studying PDEs derived from theories of higher dimensional gravity, string theory, particle physics and cosmology. My contact details are email@example.com.
- Oct. 2020 – Sept. 2023: Herchel Smith Postdoctoral Research Fellow, DPMMS, University of Cambridge.
- July 2020 – Sept. 2020: LMS Early Career Fellow, Queen Mary University London.
- Oct. 2015 – June 2020: PhD in Mathematics, University of Edinburgh. My supervisor was Pieter Blue and a copy of my thesis can be found here.
- 2010 – 2014: BA in Mathematics and MMath (Part III) at Newnham College, University of Cambridge.
Papers and preprints
- Hidden structure and sharp asymptotics for the Dirac–Klein-Gordon system in two space dimensions, with Shijie Dong, submitted.
- Stability of some two dimensional wave maps, with Shijie Dong, submitted.
- Two dimensional wave–Klein-Gordon equations with semilinear nonlinearities, with Shijie Dong, submitted.
- Global stability of spacetimes with supersymmetric compactifications, with Lars Andersson, Pieter Blue and Shing-Tung Yau, submitted.
- Stabilizing relativistic fluids on spacetimes with non-accelerated expansion, with David Fajman and Todd Oliynyk, Communications in Mathematical Physics, 383 (2021) 401-426.
- Global evolution of the U(1) Higgs Boson: nonlinear stability and uniform energy bounds, with Philippe LeFloch and Shijie Dong, Annales Henri Poincaré, Vol 22 (2021) 677–713.
- Attractors of the Einstein-Klein-Gordon system, with David Fajman, Communications in Partial Differential Equations, Vol. 46 Issue 1 (2021) 1-30.
- Stability of a coupled wave-Klein-Gordon system with quadratic nonlinearities, with Shijie Dong, Journal of Differential Equations, Vol. 269 Issue 9 (2020) 7470-7497.
- The Weak Null Condition and Kaluza-Klein Spacetimes, Journal of Hyperbolic Differential Equations, Vol. 15, No. 2 (2018) 219-258.
Awards, grants and fellowships
- 2021, Certificate of Commendation, Edinburgh Mathematical Society PhD Thesis Prize.
- 2020, London Mathematical Society Early Career Fellowship to visit Prof. David Berman at QMUL.
- 2020, REWIRE Grant and Fellowship at University of Vienna (€200,000, declined for Herchel Smith position).
- 2020, Henslow Junior Research Fellowship, Darwin College Cambridge (declined for Herchel Smith position).
- 2019, Laura Wisewell Travel Scholarship, University of Edinburgh.
- 2018, Sir William Darling Memorial Prize, University of Edinburgh, for my maths outreach work.
- 2017, Postgraduate Research Student Essay Prize, top grade, University of Edinburgh.
- 2015, funded PhD positions at the University of Cambridge (declined) and MIGSAA (UoE and HWU).
- 2014, Anne Clough Prize for excellent exam performance, Newnham College, University of Cambridge.
- 2013, Marjorie Tunnicliffe Prize for excellent exam performance, Newnham College, University of Cambridge.
Invited research visits
- 2022, ESI Programme on “Mathematical Perspectives of Gravitation beyond the Vacuum Regime”, Austria.
- 2021, Workshop on “Mathematical Aspects of General Relativity”, Oberwolfach.
- 2020, “Hyperbolic Differential Equations in Geometry and Physics” at the MATRIX research institute, Australia. (Postponed)
- 2019, Institut Mittag-Leffler fellowship (2 month visit), Sweden.
- 2018 – 2019: 6 month research visit to the Gravitational Physics group at the University of Vienna working under Associate Professor David Fajman.
- 2017 – 2018: 3 research visits (totalling 8 months) to Sorbonne-UPMC, Paris working under Professor Philippe LeFloch.
Other maths projects
- I wrote a 2 page summary of my Kaluza-Klein paper for the UoE School of Maths Postgraduate Research Student Essay Prize.
- In my first year MIGSAA project I showed the non-linear stability of dimensional Minkowski spacetime for (up to some finer points regarding initial data).
- In my Part III essay in 2014 I generalised the proof of local well-posedness of BSSN to high dimensions, for . This was actually not known before then.