For seminal contributions in regularity theory of nonlinear partial differential equations, free boundary problems, fully nonlinear equations, and nonlocal diffusion.

For advances in physical applied mathematics and in mathematics applied to physical systems.

For advances in scalable implicit methods for linear and nonlinear partial differential equations and wide application in science and engineering.

For contributions to stochastic, adaptive and large scale systems.

For contributions to analysis and algorithms for differential algebraic equations.

For pioneering work in mathematics of information, compressive sensing, computational harmonic analysis, statistics, and scientific computing.

For contributions to the modeling and analysis of partial differential equations motivated by applications in the life sciences.

For contributions to signals, statistics, and mathematical finance.

For his outstanding contributions to applied mathematics in complex particle dynamics and service to the Applied Mathematics Community of the European Mathematical Society.

For contributions to numerical analysis and image processing, and for service to the mathematical community.

For advances in numerical linear algebra and imaging science, including the theory of Toeplitz solvers.

For his outstanding contributions to physical and biological modeling as well as for his asymptotic methods development in applied mathematics.

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

For contributions to inverse problems in acoustics and electromagnetic theory.

For contributions to computational fluid dynamics.

For contributions to numerical analysis and computational mechanics, particularly to the development of the mathematical theory of finite element methods and the modeling of elastic structures.

For contributions to differential equations and science policy.

For contributions to adaptive and numerical methods for partial differential equations in science and engineering.

For contributions to large-scale, sparse numerical optimization, financial optimization, and leadership in mathematics education and engagement with industry.

For pioneering and groundbreaking contributions to signal processing, tensor decompositions, and was instrumental in creating independent component analysis.

For fundamental contributions to optimization theory, software and industrial practice.

For contributions to the mathematical analysis of nonlinear partial differential equations, fluid dynamics, and turbulence.

For contributions to financial mathematics and stochastic analysis.

For contributions to the Traveling Salesman Problem and other combinatorial optimization problems.

For contributions to fluid mechanics.

For contributions to numerical methods for incompressible fluid dynamics and leadership in promoting diversity in the mathematical sciences.

For contributions to optimization under uncertainty and its implementation in industrial practice, and for leadership in mentoring young researchers.