15:30-16:05 Nick Hale, University of Oxford (currently a postdoc at SU)
Title: An algorithm for the convolution of Legendre expansions
Abstract: Convolution is widely-used and fundamental mathematical operation in signal processing, statistics, and PDE theory. Unfortunately the CONV() method in Chebfun  for convolving two chebfun objects has long been one of the most disappointingly slow features of the project. In this talk we will present a new algorithm , which shows performance gains on the order of a factor 100. The key components of the new algorithm are:
* a convolution theorem for Legendre polynomials
* recurrence relations satisfied by spherical Bessel functions
* recent developments in fast Chebyshev-Legendre transforms 
Time-permitting, we shall end with an application from statistics, using the fact that the probability distribution of the sum of two independent random variables is the convolution of their individual distributions.
 N. Hale and A. Townsend, “A fast, simple, and stable Chebyshev-Legendre transform using an asymptotic formula”, SISC, Vol. 36, No. 1, pp. A148-A167, 2014.
 N. Hale and A. Townsend, “An algorithm for the convolution of Legendre series”, SISC (to appear).
 L.N. Trefethen et al., Chebfun V4, www.chebfun.org/