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 PhD thesisLink opens in a new window, I studied sub-Riemannian diffusions, a special class of hypoelliptic diffusion processes, on manifolds.

In this workLink opens in a new window, I derived a polynomial approximation for Brownian motion and show that the associated fluctuations follow a semicircle law. As discussed in Brownian paths and random polynomialsLink opens in a new window, 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.

Brownian motion on spaces of discrete regular curvesLink opens in a new window, with Emmanuel Hartman. Electronic Communications in Probability, Vol. 31 (2026), Article No. 20, 1–11. [arXivLink opens in a new window]
Characterization of geodesic completeness for landmark spaceLink opens in a new window, with Stephen C. Preston and Stefan Sommer. Discrete and Continuous Dynamical Systems, Vol. 50 (2026), 224–240. [arXivLink opens in a new window]
Asymptotic error in the eigenfunction expansion for the Green’s function of a Sturm–Liouville problemLink opens in a new window. Constructive Approximation, Vol. 62 (2025), No. 1, 1–59. [arXivLink opens in a new window]
Jump stochastic differential equations for the characterisation of the Bragg peak in proton beam radiotherapyLink opens in a new window, 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. [arXivLink opens in a new window]
Long-time existence of Brownian motion on configurations of two landmarksLink opens in a new window, with Philipp Harms and Stefan Sommer. Bulletin of the London Mathematical Society, Vol. 56 (2024), No. 5, 1658–1679. [arXivLink opens in a new window|videoLink opens in a new window]
Intrinsic sub-Laplacian for hypersurface in a contact sub-Riemannian manifoldLink opens in a new window, with Davide Barilari. Nonlinear Differential Equations and Applications, Vol. 31 (2024), Article No. 3, 1–31. [arXivLink opens in a new window|cvgmtLink opens in a new window]
Brownian bridge expansions for Lévy area approximations and particular values of the Riemann zeta functionLink opens in a new window, with James Foster. Combinatorics, Probability and Computing, Vol. 32 (2023), No. 3, 370–397. [arXivLink opens in a new window]
Cartan connections for stochastic developments on sub-Riemannian manifoldsLink opens in a new window, with Ivan Beschastnyi and Alexandr Medvedev. The Journal of Geometric Analysis, Vol. 32 (2022), Article No. 13, 1–37. [arXivLink opens in a new window|HALLink opens in a new window]
Stochastic processes on surfaces in three-dimensional contact sub-Riemannian manifoldsLink opens in a new window, with Davide Barilari, Ugo Boscain and Daniele Cannarsa. Annales de l’Institut Henri Poincaré – Probabilités et Statistiques, Vol. 57 (2021), No. 3, 1388–1410. [arXivLink opens in a new window|HALLink opens in a new window|cvgmtLink opens in a new window]
A semicircle law and decorrelation phenomena for iterated Kolmogorov loopsLink opens in a new window. Journal of the London Mathematical Society, Vol. 103 (2021), No. 2, 558–586. [arXivLink opens in a new window]
Optimal transport, gradient estimates, and pathwise Brownian coupling on spaces with variable Ricci boundsLink opens in a new window, with Mathias Braun and Karl-Theodor Sturm. Journal de Mathématiques Pures et Appliquées, Vol. 147 (2021), 60–97. [arXivLink opens in a new window]
An explicit formula for the inverse of a factorial Hankel matrixLink opens in a new window. The Australasian Journal of Combinatorics, Vol. 79 (2021), No. 2, 250–255. [arXivLink opens in a new window]
Small-time fluctuations for the bridge in a model class of hypoelliptic diffusions of weak Hörmander typeLink opens in a new window. Electronic Journal of Probability, Vol. 24 (2019), Article No. 11, 1–19. [arXivLink opens in a new window]
Small-time fluctuations for sub-Riemannian diffusion loopsLink opens in a new window. Probability Theory and Related Fields, Vol. 171 (2018), No. 3-4, 617–652. [arXivLink opens in a new window]

Preprints

Score matching for sub-Riemannian bridge samplingLink opens in a new window, with Erlend Grong and Stefan Sommer. arXiv:2404.15258, 23 April 2024. [videoLink opens in a new window]

Proceedings

Small-time fluctuations for hypoelliptic diffusion bridgesLink opens in a new window. Oberwolfach Reports 24/2023, Hypoelliptic Operators in Geometry, 13–15.
Radial process on a model hypersurface in a contact sub-Riemannian model spaceLink opens in a new window, with Davide Barilari. Oberwolfach Reports 49/2022, Heat Kernels, Stochastic Processes and Functional Inequalities, 54–56.
A polynomial expansion for Brownian motion and the associated fluctuation processLink opens in a new window. Oberwolfach Reports 48/2021, Statistics of Stochastic Differential Equations on Manifolds and Stratified Spaces, 15–17.

Theses

Geometry of sub-Riemannian diffusion processesLink opens in a new window. PhD thesis, 2018. Available through the University of Cambridge Repository ApolloLink opens in a new window
Brownian Motion on a Riemannian ManifoldLink opens in a new window. Part III Essay for Master of Mathematics, 2013

Other writings

Sub-Riemannian diffusions. CCA mini-project, Working paper, 2014
Gaussian beams and the propagation of singularitiesLink opens in a new window, 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