Broadly speaking, my research is in the area of rigorous analysis of partial differential equations (PDE), with particular emphasis on equations of compressible fluid dynamics and self-gravitating systems, e.g. evolution of stars. I am most interested in free boundary settings, where the fluid support is allowed to change/evolve in time. Such problems are connected to fundamental questions in physics, where one tries to e.g. understand the stability/instability of special solutions (such as the steady stars or self-similar expanding/collapsing stars) and their dynamic stability properties.
Publications
- Linear Stability of liquid Lane-Emden stars. Quart. Appl. Math. 82 (2024), 639-672 (arXiv:2208.06736)
- Nonradial stability of expanding Goldreich-Weber stars (with Mahir Hadžić and Juhi Jang). Preprint, arXiv:2212.11420
Education
| 2019 – 2023 | University College London PhD in Mathematics (supervised by Prof Mahir Hadžić) |
| 2018 – 2019 | University of Cambridge MMath, with Distinction |
| 2015 – 2018 | University of Cambridge BA (Hons) Mathematics |
| 2010 – 2015 | Shaftesbury School (Shaftesbury, Dorset) A-levels & GCSEs |
Lecture notes
When I was a student at Cambridge, I edited a set of lecture notes for the Cambridge Mathematical Tripos based on the lectures given at the time and various official and unoffical lecture notes that existed at the time. It contains all courses in Part I and Part II, and a selection of mainly analysis and geometry courses in Part II and Part III. You can find them in this link.