Complexity in numerical computation:

Felipe Cucker (Universitat Pompeu Fabra, Barcelona and City University of Hong Kong)

Homotopy methods:

Tien Yien Li (Michigan State University)

Optimization: interior-point methods and nonlinear optimization

Mike Overton (New York University) & Jim Renegar (Cornell University)

Differential equations and discretized dynamical systems:

Arieh Iserles (University of Cambridge) & Andrew Stuart (Stanford University)