I am a PhD student at the University of Cambridge
under the supervision of Gabriel Paternain and member of the research group of Richard Nickl. Before this I studied at University of Bonn, University of British Columbia and MLU Halle-Wittenberg.
Department of Pure Mathematics and Mathematical Statistics
Cambridge, CB3 0BW, UK
In my research I study geometric inverse problems with a focus on their statistical properties. A typical such problem asks to determine some geometric quantity within a domain (e.g. a potential, tensor, connection, etc.) from indirect measurements at the boundary of the domain.
Many of these problems model real life tomography methods, where observations are noisy and one seeks good algorithms to recover the quantity of interest. The performance of statistical algorithms is closely tied to the analytical properties of the underlying problem - in my research I try to understand this interplay and tackle the resulting analytical challenges.
The tools I use come from differential geometry, PDE's & microlocal analysis and Bayesian non-parametric statistics.
Articles and Preprints
- The transport Oka-Grauert principle for simple surfaces
With Gabriel P. Paternain ▪ arXiv (2021)
- On log-concave approximations of high-dimensional posterior measures and stability properties of non-linear inverse problems
With Richard Nickl ▪ arXiv (2021)
- Stability of the non-abelian X-ray transform in dimension ≥ 3
J Geom Anal (2021) ▪