Research

My research lies in stochastic analysis with connections to geometry, analysis, and numerics, and with a particular interest in hypoelliptic diffusion processes on manifolds. Hypoelliptic diffusion processes 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 thesis, I study sub-Riemannian diffusions, a special class of hypoelliptic diffusion processes, on manifolds.

In a recent work, I derive a polynomial approximation for Brownian motion and show that the associated fluctuations follow a semicircle law. As discussed in Brownian paths and random polynomials, 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 ORCID iD icon

Preprints

Theses

Other writings

  • Sub-Riemannian diffusions. CCA mini-project, Working paper, 2014
  • Gaussian beams and the propagation of singularities, 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

Talks

  • Contributed talk at MASDOC-CCA conference, University of Warwick, 15-17 April 2015

Research visits

  • Prof Peter Friz at TU Berlin, 19-23 September 2016
  • Prof Karl-Theodor Sturm at Universität Bonn through a Special Exchange Grant of the SFB 1060, 25-29 April 2016

Conference attendances

  • Symposium “Stochastic Analysis” at RIMS, Kyoto University, 7-11 September 2015, attendance supported by IMU Itô Travel Award
  • 38th Conference on Stochastic Processes and their Applications, University of Oxford, 13-17 July 2015
  • MASDOC-CCA conference, University of Warwick, 15-17 April 2015
  • Random Geometry, Isaac Newton Institute Cambridge, January – July 2015