Publications
My research lies in stochastic analysis with connections to geometry, analysis, and numerics, and with a particular interest in hypoelliptic operators and hypoelliptic diffusion processes on manifolds. Hypoelliptic operators arise naturally in the study of dynamical systems where noise has a lower dimension than the dynamics it enters. Examples for such dynamical systems are constrained physical systems, where the motion of particles or objects is restricted along a set of admissible paths. In my , I studied sub-Riemannian diffusions, a special class of hypoelliptic diffusion processes, on manifolds.
In , I derived a polynomial approximation for Brownian motion and show that the associated fluctuations follow a semicircle law. As discussed in , the polynomial approximation was subsequently implemented into MATLAB by Nick Trefethen as a Chebfun Example. The last figure in that article further illustrates the semicircle law for the fluctuation process.
Publications
- , with Emmanuel Hartman. Electronic Communications in Probability, Vol. 31 (2026), Article No. 20, 1–11. []
- , with Stephen C. Preston and Stefan Sommer. Discrete and Continuous Dynamical Systems, Vol. 50 (2026), 224–240. []
- . Constructive Approximation, Vol. 62 (2025), No. 1, 1–59. []
- , with Alastair Crossley, Emma Horton, Jere Koskela, Andreas E. Kyprianou and Sarah Osman. Proceedings of the Royal Society A, Vol. 481 (2025), No. 2310, Article No. 20240687, 1-29. []
- , with Philipp Harms and Stefan Sommer. Bulletin of the London Mathematical Society, Vol. 56 (2024), No. 5, 1658–1679. [|]
- , with Davide Barilari. Nonlinear Differential Equations and Applications, Vol. 31 (2024), Article No. 3, 1–31. [|]
- , with James Foster. Combinatorics, Probability and Computing, Vol. 32 (2023), No. 3, 370–397. []
- , with Ivan Beschastnyi and Alexandr Medvedev. The Journal of Geometric Analysis, Vol. 32 (2022), Article No. 13, 1–37. [|]
- , with Davide Barilari, Ugo Boscain and Daniele Cannarsa. Annales de l鈥橧nstitut Henri Poincar茅 – Probabilit茅s et Statistiques, Vol. 57 (2021), No. 3, 1388–1410. [||]
- . Journal of the London Mathematical Society, Vol. 103 (2021), No. 2, 558–586. []
- , with Mathias Braun and Karl-Theodor Sturm. Journal de Math茅matiques Pures et Appliqu茅es, Vol. 147 (2021), 60–97. []
- . The Australasian Journal of Combinatorics, Vol. 79 (2021), No. 2, 250–255. []
- . Electronic Journal of Probability, Vol. 24 (2019), Article No. 11, 1–19. []
- . Probability Theory and Related Fields, Vol. 171 (2018), No. 3-4, 617–652. []
Preprints
- , with Stefan Sommer. arXiv:2606.02570, 1 June 2026.
- , with Erlend Grong and Stefan Sommer. arXiv:2404.15258, 23 April 2024. []
Proceedings
- . Oberwolfach Reports 24/2023, Hypoelliptic Operators in Geometry, 13–15.
- , with Davide Barilari. Oberwolfach Reports 49/2022, Heat Kernels, Stochastic Processes and Functional Inequalities, 54–56.
- . Oberwolfach Reports 48/2021, Statistics of Stochastic Differential Equations on Manifolds and Stratified Spaces, 15–17.
Theses
- . PhD thesis, 2018. Available through the University of Cambridge Repository
- . Part III Essay for Master of Mathematics, 2013
Other writings
- Sub-Riemannian diffusions. CCA mini-project, Working paper, 2014
- , with Dominic Dold and Ellen Powell. Final assignment for the CCA graduate course Analysis of Partial Differential Equations, 2014
- Numerical evolutions of spherically symmetric spacetimes with the modified Cartoon method. CCA mini-project, Working paper, 2014