Experience Research Professor School of Mathematical Sciences, University of Science and Technology of China, September 2018 - Present Assistant Professor (tenured) School of Mathematics, Statistics, and Actuarial Science, University of Kent, August 2015 - August 2018 Postdoctoral Research Fellow Mathematical Institute, Oxford University, September 2012 - August 2015Research in numerical analysis. Core member of Chebfun project. Supervisor: Prof. L. N. Trefethen FRS Algorithm ScientistGeneral Electric Global Research, General Electric, Niskayuna, NY, USA, May 2011 to May 2012Research in scientific computing. Education PhD, Computational Mathematics New Jersey Institute of Technology & Rutgers, the State University of New Jersey, New Jersey, USA, 2010

Approximation theory Spectral methods Fast algorithms Orthogonal polynomials

Understanding the ultraspherical spectral method Cheng, L. and Xu, K.Submitted (2024) Spectral approximation of convolution operators of Fredholm type Liu, X., Deng, K., and Xu, K.Submitted (2024) A continuous approach for computing the pseudospectra of operators Deng, K., Liu, X., and Xu, K.Submitted (2024) Solving nonlinear ODEs with the ultraspherical spectral method Qin, O. and Xu, K.IMA J. Numer. Anal. 44 (2024), pp. 3749–3779. Solving time-dependent PDEs with the ultraspherical spectral method Cheng, L. and Xu, K.J. Sci. Comput. (2023), 96:70. On the backward error incurred by the compact rational Krylov linearization Chen, H. and Xu, K.J. Sci. Comput. 89 (2021), pp. 1-22. Volterra-type Convolution of classical polynomials Loureiro, A. F. and Xu, K.Math. Comp. 88 (2019), pp. 2351-2381. Spectral approximation of convolution operator Xu, K. and Loureiro, A. F.SIAM J. Sci. Comput. 40 (2018), no. 4, pp. A2336-A2355. A fast algorithm for the convolution of functions with compact support using Fourier extensions Xu, K., Austin, A. P., and K. WeiSIAM J. Sci. Comput. 39 (2017), no. 6, pp. A3089-A3106. On the numerical stability of the second barycentric formula for trigonometric interpolation in shifted equispaced points Austin, A. P. and Xu, K.IMA J. Numer. Anal. 37 (2017), pp. 1355-1374. The Chebyshev points of the first kindXu, K.Appl. Numer. Math. 102 (2016), pp. 17-30. Explicit construction of rectangular differentiation matrices Xu, K. and Hale, N.IMA J. Numer. Anal. 36 (2016), pp. 618-632. Extension of the continuum time-dependent Hartree-Fock method to proton states Pardi, C. I., Stevenson, P. D., and Xu, K.Phys. Rev. E 89 (2014), 033312. A bootstrap method for sum-of-pole approximations Xu, K. and Jiang, S.J. Sci. Comput. 55 (2013), pp. 16-39. Analytical and computational methods for two-phase flow with soluble surfactant Xu, K., Booty, M., and Siegel, M.SIAM J. Appl. Math. 73 (2013), pp. 523-548.