The fast multipole method (FMM) is a numerical algorithm for efficiently evaluating the pairwise interaction between a large number of particles. It was introduced by Greengard and Rokhlin and ranked as one of the top ten algorithms of the 20th century. This talk will give a rather geometric introduction to the essential ideas of the FMM and explain some recent work in developing directional fast multipole methods for oscillatory kernels.

Lexing Ying received his BS at Shanghai Jiao Tong University and earned a PhD degree (2004) from New York University. In 2004-2006, he was a Postdoctoral Scholar at California Institute of Technology. From 2006 to 2012, he was a professor at Department of Mathematics of The University of Texas at Austin. Since Dec 2012, he has been a Professor of Mathematics at Stanford University. His research focuses on developing efficient and accurate algorithms for numerical solution of partial differential equations and integral equations. He was awarded a Sloan Fellowship in 2007, an NSF CAREER ward in 2009, the Feng Kang prize of Scientific Computing from Chinese Academy of Sciences in 2011, and the SIAM James H. Wilkinson Prize in Numerical Analysis and Scientific Computing in 2013.