The prizes were awarded at the Opening Ceremony of the International Congress for Industrial and Applied Mathematics, ICIAM 2015, to be held 10–14 August 2015 in Beijing, People's Republic of China.

The Prize Committee was chaired by Barbara Lee Keyfitz, the then President of ICIAM.

Other members were:

- Philippe Ciarlet (ICIAM Su Buchin Prize)
- Pam Cook (ICIAM Maxwell Prize)
- Takashi Kako (ICIAM Pioneer Prize)
- Donatella Marini (ICIAM Collatz Prize)
- Felix Otto (ICIAM Lagrange Prize)

## ICIAM Collatz Prize

awarded to Annalisa Buffa (Institute for Applied Mathematics and Information Technologies, Pavia–Genoa–Milan, Italy) in recognition of her spectacular use of deep and sophisticated mathematical concepts to obtain outstanding contributions to the development of computer simulations in science and industry.

The Collatz Prize was established to provide international recognition to individual scientists under 42 years of age for outstanding work on industrial and applied mathematics.

It was created on the initiative of GAMM, and first awarded in 1999.

Carrying a cash award of USD 5000, the Collatz Prize is presently funded by GAMM.

Annalisa Buffa graduated in Computer Engineering at the University of Pavia in 1996, and got her PhD in Mathematics at the University of Milan, in 2000. In 2004 she became Research Director at the Institute for Applied Mathematics and Information Technologies (Pavia–Genoa–Milan), and (overall) Director of the Institute in 2013. She has received important grants, including an ERC Starting Grant in 2008, and prestigious awards, including the Bartolozzi Prize and the John Todd Fellowship Prize in 2007.

In a relatively short amount of time she has been able to bring fundamental contributions to a number of different aspects of scientific computing, with an incredible range both in the type of applications and in the type of mathematical instruments.

One of her major achievements is the characterization of traces of vector fields for Sobolev spaces relevant in electromagnetics: in a series of fundamental papers with Patrick Ciarlet she produced a complete characterization of the traces on the boundary of polyhedral domains. This has been a breakthrough for the understanding of the integral equation formulation of electromagnetic scattering.

Another masterpiece was the construction, together with Snorre Christiansen, of an optimal preconditioner for electromagnetic integral equations. This problem was open for a long time, and the result finally came thanks to the combination of mathematical knowledge and engineering conception that she had acquired over the years. The preconditioner is already widely used in industrial practice.

More recently, with Giancarlo Sangalli she initiated research activity on the mathematical understanding of isogeometric analysis, where she played a fundamental role in providing a mathematical foundation. She studied the mathematical structure of non-tensor-product extensions of multivariate splines addressing deep theoretical questions which will impact enormously the development of adaptive isogeometric methods. She extended the theory of exterior calculus to splines, showing how this leads to unexpected schemes for several important problems, and she has also promoted the development of free software which is now widely used in the isogeometric community.

In brief, the trademark of her work is the use of highly sophisticated mathematical techniques to produce fundamental breakthroughs that are applied to computer simulations in industry. For this she can be considered as a worthy recipient of the 2015 Collatz Prize.

The subcommittee for ICIAM Collatz Prize was:

- Donatella Marini (University of Pavia, Italy), chair;
- Tom Hou (California Institute of Technology, USA);
- Hisashi Okamoto (Kyoto University, Japan);
- Mete Soner (ETH Zürich, Switzerland);
- Andrew Stuart (University of Warwick, UK);
- Steve Wright (University of Wisconsin, USA).

## ICIAM Lagrange Prize

awarded to Andrew J. Majda (New York University, USA) in recognition of his ground-breaking, original, fundamental and pioneering contributions to applied mathematics and, in particular, to wave front propagation and combustion, scattering theory, fluid dynamics and atmosphere climate science.

The Lagrange Prize was established to provide international recognition to individual mathematicians who have made an exceptional contribution to applied mathematics throughout their careers.

It was created on the initiative of SMAI, SEMA and SIMAI and first awarded in 1999.

Carrying a cash award of USD 5000, the Lagrange Prize is presently funded by the three member societies SMAI, SEMA and SIMAI.

Andrew J. Majda is the Morse Professor of Arts and Sciences at the Courant Institute of New York University. Born in East Chicago, Indiana on 30 January 1949, he received a B.S. degree from Purdue University in 1970 and a Ph.D. degree from Stanford University in 1973. He began his scientific career as a Courant Instructor at the Courant Institute from 1973–1975. Prior to returning to the Courant Institute in 1994, he held professorships at Princeton University (1984–1994), the University of California, Berkeley (1978–1984), and the University of California, Los Angeles (1976–1978).

He is a member of the National Academy of Sciences and the American Academy of Arts and Science. His work has been honored by the National Academy of Science Prize in Applied Mathematics, the John von Neumann Prize of the Society of Industrial and Applied Mathematics, the Gibbs Prize of the American Mathematical Society and the Wiener Prize of the American Mathematical Society and the Society of Industrial and Applied Mathematics. Some of the most fundamental contributions of Majda and his collaborators in the area of wavefront propagation are the identification and study of the absorbing boundary conditions for numerical computations of the wave equation in unbounded domains, which has had major impact in the field over the last 30 years; the existence and stability analysis of multi-dimensional shock waves, which is the only available complete and general result to date about multi-dimensional systems; a model for detonation, now named for him, which has served as an important testing ground for both theoretical and numerical studies of detonation waves; and the theory of turbulent combustion, which has led to a new understanding of the effect of the environment in reaction–diffusion–combustion phenomena.

Majda has worked extensively in the general theory of fluid dynamics, where, together with his collaborators, has made important and far-reaching contributions. Among them are the celebrated Beale–Kato–Majda theorem; a necessary and sufficient condition for the regularity of solutions to the 3-D Euler equations; an extensive analysis of the behavior of the advection and diffusion of a passive scalar by incompressible velocity fields whose statistical description involves a continuous range of excited scales; a mathematically rigorous equilibrium statistical theory for three-dimensional nearly parallel vortex filaments and the by-now-classical two-dimensional surface quasi-geostrophic flow model which is used to predict the formation of sharp fronts between air masses in the atmosphere.

Majda has also made further revolutionary contributions to the development and analysis of mathematical models in atmosphere and ocean sciences. These include the multi-scale modeling and analysis of moist fluid dynamics in the atmosphere and, in particular, the tropics; the development of filtering methods for nonlinear chaotic systems; novel mathematical strategies for prediction and data assimilation in complex multi-scale systems, including new techniques for super-parametrization; reduced stochastic and statistical modeling for climate; and the development and exploitation of statistical physics methods in geophysical problems. His research, which has merged asymptotic and numerical methods, physical reasoning and modeling, along with rigorous mathematical analysis, has had an enormous and long lasting impact on modern applied mathematics, science and engineering (geophysics, seismology, weather prediction, combustion, and more) and remains the state of the art today.

The subcommittee for ICIAM Lagrange Prize was:

- Felix Otto (MPI Leipzig, Germany), chair;
- Peter Constantin (University of Chicago, USA);
- Jesús Sanz-Serna (Valladolid, Spain);
- Endre Süli (University of Oxford, UK);
- Jean Taylor (Rutgers University, USA);
- Juan Velázquez (Universität Bonn, Germany).

## ICIAM Maxwell Prize

awarded to Jean-Michel Coron (Paris, France) for his fundamental and original contributions to the study of variational methods for partial differential equations and the nonlinear control of nonlinear partial differential equations.

The Maxwell Prize was established to provide international recognition to a mathematician who has demonstrated originality in applied mathematics.

It was created on the initiative of the IMA (with the support of the J.C. Maxwell Society), and first awarded in 1999.

Carrying a cash award of USD 5000, the Maxwell Prize is presently funded by IMA.

Jean-Michel Coron of the Université Pierre et Marie Curie is the winner of the 2015 ICIAM Maxwell Prize for his fundamental and original contributions to the study of variational methods for partial differential equations and the control of nonlinear partial differential equations.

Jean-Michel Coron is a Professor in the Laboratoire Jacques-Louis Lions at the Université Pierre et Marie Curie. Born in Paris in 1956, he received an undergraduate Engineering degree from the École Polytechnique in 1978, a graduate Engineering degree from the Corps des Mines in 1981, and a Doctor of Mathematical Sciences degree from the Université Pierre et Marie Curie in 1982.

Jean-Michel Coron has had a deep and profound impact in the study of variational methods for nonlinear partial differential equations. His original work on constant mean curvature surfaces, periodic solutions for nonlinear wave equations, nonlinear elliptic equations with critical Sobolev exponents and harmonic maps for nematic liquid crystals has had a major impact in these fields. This work was crucial to the understanding of the equilibrium behavior of liquid crystals, and to research on the dynamical behavior of harmonic mappings and liquid crystals.

Jean-Michel Coron is probably best known for his original work on the control of nonlinear partial differential equations. His work on the global controllability of the two-dimensional Euler equations of incompressible fluids represents a brilliant interplay of techniques that he developed for control along nonsingular trajectories and the stabilization of finite dimensional control systems. One of the main underlying ideas is that although the linearization of the Euler equations around the trivial solution is not controllable, it is possible to construct a non-trivial trajectory such that the corresponding linearized system is controllable. He has also produced major results on the global controllability of Navier–Stokes equations for incompressible viscous fluids, the Korteweg–de Vries equations, the Saint–Venant equations, and Schrödinger models in quantum control. His work on the controllability of the Euler and Navier–Stokes equations is widely hailed as one of the most original results on the controllability of nonlinear partial differential equations.

The subcommittee for ICIAM Maxwell Prize was:

- L. Pamela Cook (Delaware, USA), chair;
- José Cuminato (São Paulo, Brazil);
- Jorge Moré (Argonne National Laboratory, USA);
- Amiya Pani (IIT Bombay, India);
- Benoît Perthame (Paris, France);
- Christoph Schwab (ETH Zürich, Switzerland).

## ICIAM Pioneer Prize

awarded to Björn Engquist (Austin, Texas, USA) for fundamental contributions in the field of applied mathematics, numerical analysis and scientific computing which have had long-lasting impact in the field as well as successful applications in science, engineering and industry.

The Pioneer Prize was established for pioneering work introducing applied mathematical methods and scientific computing techniques to an industrial problem area or a new scientific field of applications.

It was created on the initiative of SIAM, and was first awarded in 1999.

Carrying a cash award of USD 5000, the Pioneer Prize is presently funded by SIAM.

Bjorn Engquist received his PhD from Uppsala University in1975. He has been Professor of Mathematics at UCLA, and the Michael Henry Stater University Professor of Mathematics and Applied and Computational Mathematics at Princeton University. He was Director of the Research Institute for Industrial Applications of Scientific Computing and of the Centre for Parallel Computers at the Royal Institute of Technology, Stockholm. Currently he is Professor of Mathematics and Computational and Applied Mathematics at the University of Texas at Austin.

Bjorn Engquist has made fundamental contributions in the field of applied mathematics, numerical analysis and scientific computing which have had long lasting impact in the field as well as successful applications in science, engineering and industry. Some of his most important pioneering contributions include seminal work on absorbing boundary conditions (ABC), first proposed by Engquist and Majda, for numerical computation of wave propagation. These boundary conditions can be used at the boundary of the computational domain to reduce the artificial reflection of waves effectively. Owing to its simplicity and efficiency, it has been one of the most successful and widely used numerical techniques in the past 30 years and has had significant impact in practical applications such as geophysics, seismology and petroleum industry.

In a second direction, Engquist, with his collaborators, is responsible for the development and analysis of shock capturing methods for nonlinear hyperbolic conservation laws, including the well-known essentially non-oscillatory (ENO) method. These numerical methods have been widely used in computational fluid dynamics, aerospace engineering, combustion and other applications.

For the past twenty years, Engquist has been a leader in the field of multi-scale modeling and analysis, where his contributions include numerical homogenization, and the heterogeneous multi-scale method (HMM), among other results.

The subcommittee for ICIAM Pioneer Prize was:

- Takashi Kako (Tokyo, Japan), chair;
- Marsha Berger (New York, USA);
- Michael Dellnitz (Paderborn, Germany);
- Giovanni Gallavotti (Rutgers Univ., USA);
- Ulrich Langer (Linz, Austria);
- Dianne O'Leary (Maryland, USA).

## ICIAM Su Buchin Prize

awarded to Li Tatsien (Shanghai, PR China) in recognition of his outstanding contributions to applied mathematics and to the dissemination of mathematical sciences by means of an extensive series of summer schools that have had a profound influence on the development of research and teaching in developing countries.

The Su Buchin Prize was established to provide international recognition of an outstanding contribution by an individual in the application of Mathematics to emerging economies and human development, in particular at the economic and cultural level in developing countries.

It was created on the initiative of the CSIAM, and is being awarded for the third time.

Carrying a cash award of USD 5000, the Su Buchin Prize is presently funded by CSIAM.

Professor Li Ta-tsien is one of the most renowned specialists, worldwide, in the theory and numerical analysis of nonlinear hyperbolic partial differential equations, a domain where major difficulties abound, as well as a domain of fundamental importance in applications. These include in particular nonlinear elasticity and gas dynamics. Guided by the objective of acquiring a better understanding of the theory and physics of shocks that occur in gas dynamics, Li Ta-tsien developed a theory of local existence for classical and discontinuous solutions of the most general quasi-linear hyperbolic systems in two variables, posing them as problems where a free boundary occurs. In this fashion, he was able to specify the local structure of discontinuous solutions. This pioneering work initiated new directions for research in the subject.

In another series of fundamental contributions, Li Ta-tsien established the existence of classical solutions for the Cauchy problem for general quasi-linear hyperbolic systems, with sufficiently small initial data. This work constitutes a double achievement: First, it provides optimal estimates of lower and upper bounds for the life-span of a classical solution; second, it can be applied to the system of nonlinear elastodynamics. Jean Leray, one of the most famous mathematicians of the twentieth century, commented, "The work of Li Ta-tsien provides precise and elegant answers to manifold questions raised by many researchers".

More recently, Li Ta-tsien was able to obtain the first satisfactory mathematical modeling of "resistivity well-loggings", a method of fundamental importance in petroleum exploitation. This work led him to introduce a new family of boundary value problems, called "boundary value problems with equipotential surface". He then studied such problems, both theoretically and numerically, in particular by successfully applying homogenization theory to the modeling of an electrode composed of many parts. It is a measure of the success and power of his approach that it is currently used in more than ten petroleum fields over the world!

Li Ta-tsien is not only an eminent mathematician. During the past decades, he has been extremely influential in the development of the pure and applied mathematical community in developing countries. More specifically, a very far-sighted initiaitive was taken in 1998 by Jacques-Louis Lions and Li Ta-tsien, who together co-founded ISFMA, the Institut Sino–FranÃ§ais de Mathematiques Appliqéees, or Chinese–French Institute of Applied Mathematics. Thanks to his tireless efforts, this Institute, which is beautifully housed on the campus of Fudan University, organizes every year highly successful Summer Schools, with the support of CIMPA (International Centre for Pure and Applied Mathematics in Nice, France) and other organizations. These Summer Schools regularly attract students coming from Asian countries, such as China, Thailand, Vietnam, Malaysia, Indonesia, and others. At each Summer School, the lecture notes are edited by Li Ta-tsien and published. The summer schools and their proceedings have had a profound influence and impact on the dissemination of contemporary research in the targeted countries. They have also contributed greatly to the training of countless teachers from the universities in these countries.

Through his far-sighted leadership and broad vision, Li Ta-tsien has considerably contributed to the promotion and development of "modern" pure and applied mathematics in developing countries.

The subcommittee for ICIAM Su Buchin Prize was:

- Philippe Ciarlet (Kowloon, Hong Kong), chair;
- Susanne Brenner (Louisiana, USA);
- Raymond Chan (Hong Kong, China);
- George Dinca (Bucharest, Romania);
- Mythily Ramaswamy (Bangalore, India).