Dr Sheehan Olver
F07  Carslaw Building
The University of Sydney
Telephone  9351 5782 
Fax  9351 4534 


Website 
Personal web page 
Research interests
· Integrable systems 

Important physical equations — including shallow water waves, nonlinear optics and others — have the property that they are integrable. One aspect of integrability is that the equations can be reduced to Riemann–Hilbert problems: boundary value problems in the complex plane. By solving Riemann–Hilbert problems numerically, solutions to integrable systems can be calculated accurately for arbitrarily large time. 

· Random matrix theory 

The core of random matrix theory is spectral analysis of large random matrices. Such matrices are crucial to the study of large systems of particles that repulse each other. By developing numerical methods for complex analytical structures that underly random matrices, finite dimensional statistics and statistics of algebraic manipulations of random matrices are calculable. 

· Spectral methods 

Spectral methods are numerical methods for solving differential equations globally. They have the remarkable property that they converge to the true solution exponentially fast. By using specially constructed bases, spectral methods can be designed that involve only sparse, wellconditioned linear systems, allowing for efficient computations that require as many as a million unknowns. 

· Oscillatory integrals and differental equations 

High oscillation plagues traditional numerical methods, because the oscillations must be resolved. These difficulties are avoidable by incorporating asymptotics into numerical schemes, so that the oscillations are completely removed. 
Teaching and supervision
Timetable
Awards and honours
2012 Adams Prize
2012 Carl–Erik Fröberg Prize
2013 Cherry Ripe Prize
Selected grants
2013
 Numerical Methods for InverseScattering and Stability of Nonlinear Waves; Miller P, Olver S; DVC Research/International Research Collaboration Award (IRCA).
 A new class of fast and reliable spectral methods for partial differential equations; Olver S, Olver S; Australian Research Council (ARC)/Discovery Early Career Researcher Award (DECRA).
Selected publications

RiemannHilbert Problems, Their Numerical Solution, and the Computation of Nonlinear Special Functions (Society for Industrial and Applied Mathematics (SIAM), 2016)

























