Dr. Michael O Neil

Biography

Michael O'Neil is an Assistant Professor in the Department of Mathematics at New York University. He obtained his Ph.D. in Applied Mathematics from Yale University in 2007, having previously received an M.Phil. in the same field in 2005 and an A.B. in Mathematics from Cornell University in 2003. His research interests include classical partial differential equations and their applications in mathematical physics, particularly in areas such as electromagnetics, fluids, acoustics, and heat flow. O'Neil's work involves reformulating these equations in equivalent integral equation form and developing rapid numerical solutions to these integral equations. He utilizes advanced tools such as quadrature, singular functions, and robust methods to tackle complex geometries and improve computational efficiency through fast algorithms and dense linear algebra techniques like butterfly schemes and fast multipole methods. Additionally, he applies these fast algorithms and analytical techniques to problems in computational statistics, especially focusing on Gaussian processes.

Research Interests