I am a PIMS-Simons Postdoctoral Fellow working with the group of Christoph Ortner at the University of British Columbia. Previously I held a postdoctoral research associate position at the University of Oxford after having completed a PhD in applied mathematics at the Imperial College London.
My research focus is the development of computational tools for PDEs, integral equations and fractional differential equations with applications in the natural sciences such as quantum physics and collective behavior in biology, including specifically also machine learning models thereof. I am also more generally interested in computational orthogonal polynomials and their applications in such methods.
Many physical and biological systems can be accurately modeled using atomistic many body interactions. Machine learning based methods allow one to infer succesful models for otherwise prohibitively large and complex systems.
I work on novel methodologies and applications of such frameworks as well as the closely related problem of analyzing their theoretical foundations.
Fractional differential equations generalize ODEs and PDEs to include derivative operators of non-integer order. The resulting operators are generally nonlocal and thus pose several challenges to conventional numerical approaches.
Fractional PDEs appear in natural science applications featuring memory effects, e.g. photoacoustic imaging in medical physics.
Orthogonal polynomials can be used to accurately and efficiently approximate functions.
Alongside their use in quadrature methods they can be used to construct spectral methods for solving integral as well as partial differential equations with sparse discretisations and spectral convergence.
Equilibrium measure problems arise in the continuous mean-field limit of attractive-repulsive particle systems and have diverse applications ranging from swarming behavior in animals to self-assembly properties of particle systems.
As power law interactions involve Riesz potentials, this special case also relates to fractional differential equations.
Strang splitting methods have been successfully used for the numerical treatment of magnetic Schrödinger equations in their appropriate 3D context.
I have worked towards extending these results to also work for relativistic equations which account for quantum mechanical spin.