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.

A professor in the department of mathematics at the Courant Institute, Greengard's research interests are in applied and computational mathematics, partial differential equations, computational chemistry, and mathematical biology. In 2013 Greengard was named Director of the Simons Center for Data Analysis. Greengard received the Leroy P. Steele Prize from the American Mathematical Society in 2001 and was elected to the National Academy of Sciences and the National Academy of Engineering in 2006. He holds a B.A. in mathematics from Wesleyan University, an M.D. from the Yale School of Medicine, and a Ph.D. in computer science from Yale University.