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I am a Postdoctoral Research Associate in the Numerical Analysis of Nonlocal PDEs in the group of José A. Carrillo at the University of Oxford. My research focus is on numerical analysis and the development of computational tools for integral equations, PDEs and fractional differential equations with applications in the natural sciences. I am also more generally interested in computational orthogonal polynomials and their applications in the development of multivariate spectral methods.
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.
Orthogonal polynomials can be used to accurately and efficiently approximate functions.
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