During the last few decades, fast algorithms have brought a variety of large-scale modeling tasks within practical reach. This is particularly true of integral equation approaches to electromagnetics, acoustics, gravitation, elasticity, and fluid dynamics. The practical application of these methods, however, requires analytic representations that lead to well-conditioned linear systems, techniques for error estimation that permit robust mesh refinement, and implementations on high-performance computing platforms. I will give an overview of recent progress in these areas with a particular emphasis on wave scattering problems in complex geometry. 

Leslie Greengard received his B.A. degree in Mathematics from Wesleyan University in 1979, and his Ph.D. degree in Computer Science and M.D. degree from Yale University in 1987.  From 1987-1989 he was an NSF Postdoctoral Fellow at Yale University and at the Courant Institute of Mathematical Sciences, NYU, where he is a member of the faculty. He served as the Director of the Courant Institute from 2006-2011. Greengard is also Professor of Electrical and Computer Engineering at NYU’s Tandon School of Engineering and the Director of  the Center for Computational Mathematics at the Flatiron Institute, a division of the Simons Foundation. Much of Greengard’s research has been aimed at the development of fast algorithms and high-order accurate methods for problems in scientific computing. He is a member of the National Academy of Sciences, the National Academy of Engineering and the American Academy of Arts and Sciences.