For contributions to dynamic game theory and application to robust control of systems with uncertainty.

For contributions to numerical linear algebra and its applications, especially sparse linear systems and preconditioning.

For contributions to the dynamics and control of mechanical systems.

For contributions to numerical partial differential equations, especially least-squares finite element methods, stabilized finite element methods, and software.

For contributions to linear algebra and combinatorics.

For contributions to the mathematical analysis of partial differential equations, fluid mechanics, hyperbolic systems of conservation laws, and shock waves.

For contributions to applied dynamical systems and mathematical biology, in particular the theory of coupled oscillators and neural pattern formation.

For contributions to the understanding of the stability and convergence properties of the finite element method, and for service to the numerical analysis community.

For contributions to computational biofluid dynamics and applications.

For pioneering efforts in the development and deployment of polynomial splines and constrained data fitting in the aerospace industry.

For contributions to integrable and nearly integrable partial differential equations, material science, and to polymeric, liquid crystalline, and biological and biomedical fluid mechanics.

For contributions to applied mathematics through research, editorial work, and conference organizing, and for serving as a role model for young people, especially young women.

For contributions to analytical and numerical methods for statistical transport problems in complex particle systems.

For fundamental contributions to the constructive theory of orthogonal polynomials with applications to approximation theory.

For contributions to nonlinear, discrete, and convex optimization.

For contributions to numerical linear algebra, including the LAPACK project.

For contributions to graph theory.

For contributions to combinatorial and parallel algorithms in scientific computing.

For contributions to computational science and engineering, high performance computing applications, and leadership in industrial mathematics.

For contributions to machine learning, in particular variational approaches to statistical inference.

For pioneering the mathematics of cardiac electrophysiology, elucidating scroll waves, the bidomain equations, and the mechanism of defibrillation.

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 mathematical biology.

For advances in mathematics applied to fluid dynamics, solidification, and the interaction of the two, using sharp and diffuse interface theories.

For broad and deep investigations of nonlinear dynamical systems, which highlight both theory and application.

For contributions to integration, optimization, and modeling techniques for the study of biomolecular structure and function.

For contributions to the design, analysis, and application of efficient discrete optimization algorithms in scheduling, facility location, networks, and sustainability.

For contributions to the analysis of bifurcations in the presence of symmetry.

For contributions to domain decomposition, developing the powerful software package PETSc, and simulating complex scientific and engineering phenomena on massively parallel architectures.

For contributions to computational fluid dynamics and in particular, development of adaptive algorithms.

For analytical and computational studies of nonlinear partial differential equations with applications to fluid mechanics and geophysics.

For contributions to technologies for exoplanet searches and to interior-point methods for nonlinear optimization.

For contributions to matrix analysis, numerical analysis, complex variables, and approximation theory.

For development of conceptual and physical aspects of modeling dynamical systems.

For contributions to stochastic control and financial mathematics.

For fundamental contributions to nonlinear waves.