About

My research interests are in fast algorithms for computations with orthogonal polynomials, including spectral methods for differential and integral equations, fast computation of Gauss quadrature nodes and weights, and fast polynomial transforms. See my publications list for further details.

Much of my previous work was in adaptive spectral methods for numerical solutions of PDEs; combining complex analysis, barycentric interpolation, and conformal mapping. This topic was central to my Oxford DPhil thesis, which I continued during a PostDoc at the Oxford Centre for Collaborative and Applied Mathematics (OCCAM). I also have an interest in the application of conformal mapping to quadrature methods, and the computation of certain matrix functions by complex contour integrals. I completed my DPhil (PhD) at St Hugh's College, in 2009. A copy of my CV can be found here.

I am involved in the open-source Chebfun project, and was a lead developer of version 5 and was part-funded by The MathWorks as the director of the project for two years. Chebfun is a software system written in object-oriented MATLAB, which extends familiar powerful methods of numerical computation to continuous or piecewise-continuous functions. One of its key aims is to provide a link between symbolic and numeric computing. You can find out more at www.chebfun.org

Recently, with Dan Fortunato (Flatiron institute) and Alex Townsend (Cornell), I developed the ultraSEM software, based on the ultraspherical spectral element method; a sparse spectral element method based on the hierarchical Poincare–Steklov scheme suitable for hp-adaptivity with very high p.

Teaching

• NM262 Numerical methods (Engineering)

• TW244 Applied Differential Equations (Science) 

• TW324 Numerical methods (Science)

• TW776/876 Numerical linear algebra (Applied Maths (Hons) & Engineering (MEng))

Software