For contributions to variational inequalities and fluid and solid mechanics.

For contributions to combinatorial optimization, and in particular to the design and analysis of approximation algorithms.

For contributions to operator theory.

For fundamental contributions in the design, analysis, and implementation of algorithms for network optimization problems.

For extraordinary interdisciplinary work on the mathematics of sea ice.

For contributions to nonlinear, discrete, and convex optimization.

For contributions to coding theory, data encryption, communications, and mathematical games.

For contributions to nonlinear dynamics and bifurcation theory.

For contributions to interior point methods for continuous optimization.

For contributions to nonlinear elasticity and theories of biological growth.

For her contribution to strong-stability-preserving time discretizations and other schemes for hyperbolic equations, and for her professional services including those to SIAM and women in mathematics.

For contributions to numerical continuous optimization.

For contributions to discrete mathematics and its applications.

For contributions in computer-aided geometric design and leadership in industrial mathematics.

For contributions to theoretical and numerical linear algebra.

For creation of the Fast Multipole Method and other fast algorithms.

For contributions to scientific computing, especially in numerical linear algebra and its applications.

For fundamental contributions to algorithmic differentiation and to iterative methods for nonlinear optimization.

For contributions to combinatorics and graph theory.

For contributions to numerical linear algebra, including communication-avoiding algorithms.

For contributions to combinatorial optimization and discrete mathematics.

For contributions to algorithms and software for high performance scientific computing, including the development of MPI.

For contributions to theoretical and computational dynamical systems and mathematical neuroscience.

For innovative contributions to computational fluid mechanics and fundamental contributions to the development and teaching of the finite element methods.

For stellar contributions to mathematical biology, particularly the modeling of epidemics, and applications to other public health problems.

For contributions to control of fluids and scientific computing.

For contributions to statistical mechanics, combinatorics and their connections.

For contributions in computational inverse problems, differential equations, statistical and optimization techniques, deep learning, and multi-scale methods.

For contributions to optimal control, optimization theory, and numerical optimization algorithms.

For contributions to numerical ordinary differential equations and geometric integration.

For contributions to applied dynamical systems including the theory of Lagrangian coherent structures.

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

For contributions to algorithms for rank-deficient and discrete ill-posed problems and regularization techniques.

For leadership in theoretical ecology, helping to lay the foundation for scientifically-based agriculture and resource management.

For contributions in computational science and engineering, especially parallel computing.

For contributions to graph theory.

For contributions to combinatorial and parallel algorithms in scientific computing.

For contributions to the mathematical foundations of signal processing and data science.

For research, leadership, and community building in software and algorithms for scientific and high-performance computing.

For advances in high-order numerical methods for partial differential equations and applications.

For contributions to numerical analysis and stochastic computation.

For contributions to numerical linear algebra and rounding error analysis.

For contributions to the stability analysis and control of dynamical systems.

For contributions to theoretical and numerical optimization, and for their application.

For contributions to the design and analysis of approximation algorithms, flow problems, and their innovative use in applications, and in solving NP-hard problems.

For contributions to nonlinear partial differential equations and related fields, to research administration, and to the dissemination of mathematics.

For contributions to nonlinear dynamics spanning the range from theory to applications.

For contributions to computational biology, numerical relativity, and scientific computation.

For advances in the design and analysis of algorithms.

For contributions to fluid mechanics and multiscale analysis.

For contributions to mathematical ecology and in particular the theory of the chemostat and competing species in ecology.

For contributions to network flows, integer programming, and combinatorial algorithms.

For contributions to the analysis of nonlinear stochastic signals and applications in science and engineering.

For the development of finite element methods for solid, structural, and fluid mechanics.

For contributions to the numerical solution of partial differential equations and modeling of biological systems.

For contributions to numerical linear algebra, perturbation theory, and applications.

For contributions to linear programming and optimization.

For innovative contributions to mathematical modelling in cancer biology and for the advancement of underrepresented minorities in science.

For contributions to the mathematical foundations of quantum field theory.

For contributions to relaxation schemes, numerical algorithms for kinetic equations and high frequency wave propagation.

For contributions to scientific computing and visualization.

For contributions to combinatorial optimization and its application to logistical problems.

For contributions to algorithms and complexity theory.

For contributions to dynamical systems, nonlinear partial differential equations, and applications in nonlinear optics, ocean dynamics, and neuroscience.

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 contributions to our understanding of matrix pencils and for leadership within the European high performance computing community.

For contributions to linear algebra, systems, and control and their applications in engineering.

For contributions to differential equations and dynamics.

For investigations of nonlinear dynamics and pattern formation.

For contributions to stochastic modeling, spectral elements, and fluid mechanics.

For contributions to the theory of algorithms and the theory of NP-completeness.

For contributions to wave propagation, nonlinear dynamics, optical fibers and waveguides, and computational neuroscience.

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

For contributions in many areas of applied mathematics.

For contributions to nonlinear equations, optimization, and flow in porous media.

For contributions to interactive parallel computing, matrix-based graph algorithms, green supercomputing, and big data.

For research contributions in chemical engineering, applied mathematics, and the computational sciences.

For fundamental contributions to the existence, stability, and dynamics of nonlinear waves with applications to atomic, optical, and materials physics.

For contributions to implicit methods for the solution of partial differential equations and dedicated service to the scientific community.

For advances in hyperbolic conservation laws and the study of shock waves.

For her fundamental contributions to numerical linear algebra and scientific computing, including ill-posed problems, tensor decompositions, and iterative methods.

For contributions to shape reconstruction, image processing, and geometric analysis.

For contributions to nonlinear partial differential equations, the calculus of variations, and mathematical aspects of materials science.

For contributions to asymptotic methods and systems biology.

For contributions to modeling pathogen-host interactions and host immune response in infectious diseases and training in mathematical biology/immunology.

For contributions to stochastic and non-autonomous dynamical systems.

For contributions to pattern formation and nonlinear dynamics, bifurcation theory and fluid dynamics.

For contributions to the analysis of algorithms, exceptionally influential books, and the creation of TeX.

For contributions to computational mathematics and development of numerical methods for eigenvalue problems.

For contributions to nonlinear partial differential equations, calculus of variations, phase transformations, and composite materials.

For contributions to semidefinite optimization and complementarity problems.

For contributions to numerical algorithms and software in multi-linear algebra, optimization, and graph analysis.

For contributions to dynamical systems theory and mathematical neuroscience.

For pioneering work in numerical methods and high-performance computing, multiscale modeling and computational fluid dynamics, and computational biology.

For contributions to control and estimation of nonlinear dynamical systems and stochastic processes.

For contributions in numerical linear and multilinear algebra and scientific computing.

For contributions to the analysis of problems of electromagnetics and heating.

For seminal contributions to control of nonlinear and distributed parameter systems.

For landmark contributions to mathematical physics and inverse problems.

For seminal contributions to game theory and to linear and nonlinear programming, and for leadership of SIAM in its early years.

For contributions to data mining and high performance computing.

For contributions to inverse problems, approximation to infinite dimensional control systems, and computational methods.

For contributions to stochastic control theory.

For contributions to the theory of stochastic and nonlinear dynamics and its application, and for promoting equity and diversity in mathematics.

For contributions to applied harmonic analysis, compressed sensing, and imaging sciences.

For contributions to applied dynamical systems, machine learning, and nonlinear optics.

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 the development of practical cryptography and for leadership in the mathematical community.

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 leadership in applied mathematics education, especially in mathematical modeling, across the entire educational spectrum.

For contributions to variational analysis and nonsmooth optimization.

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

For contributions to sparse linear algebra and high performance computing.

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 the advancement of mathematics within the geosciences, multiscale and operator-splitting numerical methods, and open-source software tools.

For pioneering contributions to numerical multilinear algebra, and for introducing high-level algebra, geometry, and topology to applied mathematics.

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

For significant contributions to our understanding of the properties of solutions throughout nonlinear partial differential equations.

For contributions to systems and control.

For contributions to the mathematics of materials and their translation to engineering applications.

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.

For contributions to the theory and algorithms for low-dimensional models and their applications in computer vision and image processing.

For contributions to dynamics and biology.

For contributions to mathematical biology.

For contributions to partial differential equations and their physical applications.

For seminal contributions to the theory and algorithms of optimization and applications to machine learning.

For contributions to mathematical biology, including behavioral ecology, conservation biology, fisheries management, and the biology of stem cells.

For contributions to iterative methods for linear systems and numerical methods for partial differential equations.

For contributions to high performance computing algorithms and software systems for network science and public health epidemiology.

For contributions to the theory of partial differential equations and conservation laws.

For contributions to control and systems theory.

For contributions to the development and clinical translation of cardiovascular patient-specific modeling, optimization, uncertainty and simulation methodology, and open source software development.

For contributions to mechanics, control, and dynamical systems.

For contributions to the numerical solution of partial differential equations and to the development of randomized algorithms for matrix computations.

For contributions to asymptotic and perturbation methods, bifurcation theory, nonlinear dynamics, pattern formation, stochastic dynamical systems and combustion theory.

For discerning analysis of fundamental problems in partial differential equations and mathematical fluid mechanics including boundary layers, transport, and mixing.

For contributions to numerical partial differential equations, especially multigrid and first-order system least-squares methods.

For contributions to the control for nonlinear systems.

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

For contributions to scalable numerical algorithms and software libraries for solving large-scale scientific and engineering problems.

For mathematical contributions to the underpinnings of telecommunications products and his support of SIAM.

For contributions to dispersive waves and the analysis of behaviors of nonlinear systems.

For contributions to nonlinear analysis in inverse problems.

For contributions to numerical linear algebra, matrix theory, differential-algebraic equations, mathematical software, and the transfer of knowledge to and from industry.

For contributions to theory and applications of linear algebra.

For contributions to optimization methods and software applied to challenging real-world problems, technical leadership, and service to the SIAM community.

For sustained innovation at the dynamical systems theory/applications interface; notably for advances in the use of Koopman operator theory.

For contributions to theoretical and computational fluid dynamics, especially interface problems in multiphase flows.

For contributions to the modeling and analysis of composite materials.

For contributions to nonlinear wave propagation and mathematical neuroscience.

For contributions to graph theory and computing, in particular structural, topological, and algebraic graph theory.

For contributions to numerical analysis and software, including the invention of MATLAB.

For contributions to inverse scattering and the development and analysis of finite element methods for problems in acoustics and electromagnetism.

For impactful industrial application of mathematical modeling in oncology, immunology, and virology. For mentoring, teaching, and leadership.

For contributions to partial differential equations and applications.

For contributions to variational analysis, optimization, and optimal control.

For contributions to modeling, approximation, and control design for distributed parameter systems.

For contributions to numerical methods for partial differential equations.

For advances in algorithms and software for continuous optimization.

For contributions to pattern theory and the understanding of vision.

For contributions to the computational science of image reconstruction.

For pioneering contributions to uncertainty quantification and the use of Bayesian methods in physical modeling, with applications to combustion and far beyond.

For contributions to scheduling methodology and large-scale combinatorial optimization problems.

For leadership in international applied and industrial mathematics.

For contributions to the mathematical analysis of waves and pattern formation.

For contributions to the development, analysis, and application of sparse matrix algorithms for solving large-scale scientific and engineering problems.

For fundamental contributions to algorithms for structured linear systems and image processing.

For contributions to the numerical analysis of systems, control, and data assimilation.

For research and mentoring contributions spanning applied and computational mathematics and developmental cell biology.

For contributions to the theory and practice of continuous optimization.

For contributions to the study of free boundary problems and phase transitions.

For contributions to linear algebra, regularization, and applications.

For contributions to asymptotics and singular perturbations.

For leadership of industrial applied mathematics study groups.

For advances in finite element analysis and computational mechanics.

For developing new geometric methods for differential equations leading to applications in fluid mechanics, elasticity, quantum mechanics, and image processing.

For contributions to the simulation of reactive flows and other complex processes.

For contributions to numerical analysis and optimization.

For contributions to the numerical solution of partial differential equations, level set methods, and image processing.

For contributions to theory and computational methods for dynamical systems.

For contributions to mathematical biology, in particular the theory of pattern formation in biological systems.

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

For advances in numerical optimization and eigenvalue problems.

*Deceased