For contributions to the theory of wavelets and harmonic analysis, and to interior-point and direct search optimization.

For contributions to matrix analysis and its applications to vibrations, systems theory and control.

For fundamental contributions to control theory of partial differential equations and their dissemination through numerous invited talks, administrative positions in professional societies, and the mentoring of many PhD students and postdoctoral associates.

For contributions to global polynomial optimization and the generalized problem of moments.

For contributions to the numerical solution of problems in control and filtering.

For contributions to discrete and polynomial optimization and revealing interactions between them.

For contributions to conservation laws, scattering theory, integrable systems, and numerical analysis.

For contribution to numerical analysis and scientific computing, particularly for conservation laws.

For contributions to the design of networks and circuits and for technology for Web content delivery.

For enduring influence on parallel computing systems and their adoption into mainstream use through scholarly research and development.

For contributions to optimal control with biological and physical applications and for contributions to undergraduate research.

For contributions to the control of underwater vehicles and the coordination of ensembles of independent agents, and for fundamental work in understanding the organization of animal schools and swarms.

For contributions to the understanding of how large-scale behaviors emerge from dynamics or structures on small-scales.

For contributions to mathematical biology and ecology.

For contributions to variational analysis and nonsmooth optimization.

For contributions to sparse linear algebra and high performance computing.

For contributions to mathematical biology and the study of spatial dynamics processes.

For contributions to large-scale nonlinear optimization.

For advances in the development of fast and scalable sparse matrix algorithms and fostering their use in large-scale scientific and engineering applications.

For contributions to numerical methods for partial differential equations and integral equations.

For contributions to systems and control.

For advances in the theory of shock waves and kinetic theory.

For advances in analysis of weak solutions of incompressible Euler equations and for advancing applied mathematics in Brazil and internationally.

For the development of novel applied mathematics ideas and methods for signal processing and digital communication.

For contributions to multiscale numerical methods for materials with microstructure and defects and atomistic to continuum models.