# AMS-SIAM Norbert Wiener Prize in Applied Mathematics

*SIAM and the American Mathematical Society (AMS) jointly award the Norbert Wiener Prize in Applied Mathematics for an outstanding contribution to applied mathematics in the highest and broadest sense. The recipient must be a member of one of these two societies. The prize was established in 1967 in honor of Norbert Wiener and endowed by a fund from the Department of Mathematics at the Massachusetts Institute of Technology. The endowment was further supplemented by a generous donor. The 2019 Norbert Wiener Prize is awarded to Marsha Berger (New York University) and Arkadi Nemirovski (Georgia Institute of Technology).*

Berger is being recognized for her fundamental contributions to adaptive mesh refinement (AMR) and Cartesian mesh techniques by automating the simulation of compressible flows in complex geometry.

AMR algorithms can improve the accuracy of a partial differential equation’s solution by locally and dynamically resolving a simulation’s complex features. Berger helped invent AMR. She introduced the block-structured approach to AMR in her Ph.D. thesis and later developed the Berger-Oliger algorithm and the Berger-Colella algorithm with Joseph Oliger and Phillip Colella respectively. Berger provided the mathematical foundations, algorithms, and software that allowed the solution of many otherwise intractable simulation problems, including those related to blood flow, climate modeling, and galaxy simulation. She is part of the team that created Cart3D, a NASA code based on her AMR algorithms that is extensively used for aerodynamic simulations and was instrumental in understanding the Space Shuttle Columbia disaster.

Berger received her Ph.D. in computer science from Stanford University in 1982. She conducted postdoctoral research at New York University’s Courant Institute of Mathematical Sciences and is currently a Silver Professor of Computer Science and Mathematics in the institute’s Computer Science Department, where she has been since 1985.

Berger’s honors include membership in the National Academy of Sciences, the National Academy of Engineering, and the American Academy of Arts and Sciences. She is also a Fellow of SIAM. Berger was the 2004 recipient of the Institute of Electrical and Electronics Engineers Computer Society’s Sidney Fernbach Award, and was part of the team that won NASA’s 2002 Software of the Year Award for its Cart3D software.

Upon learning of her receipt of the Norbert Wiener Prize, Berger expressed her delight and extended her gratitude to colleagues. “What a thrill to learn that I will be one of the recipients of the 2019 Norbert Wiener Prize,” she said. “One of the main enjoyments of my research is developing tools that others can use to solve real problems in aerodynamics, tsunami modeling, etc. This has been possible because of the collaborators I have been fortunate to meet, starting with Phil Colella and Antony Jameson, and later Randy LeVeque and Michael Aftosmis, along with a number of postdocs.”

“I am particularly pleased that this kind of research is being recognized,” she continued. “The AMR and Cartesian grid projects have both required the creation of new techniques in mathematics and computer science. They were decade-long efforts during which my colleagues and I developed theory and algorithms while paying attention to important practical aspects of their use in realistic geometries. Complicated algorithms have complicated implementations, and accuracy, robustness, and performance are all essential parts of the research.”

Nemirovski is being honored for his fundamental contributions to high-dimensional optimization and discovery of key phenomena in the theory of signal estimation and recovery.

A powerful and original developer of the mathematics of high-dimensional optimization, Nemirovski—along with David Yudin—invented the ellipsoid method that Leonid Khachiyan used to show (for the first time) that one can solve linear programs in polynomial time. With Yurii Nesterov, he extended interior point methods in the style of Narendra Karmarkar to general nonlinear convex optimization. This foundational work established that 33 semidefinite programs, a rich class of convex problems, are solvable in polynomial time; nowadays researchers routinely use semidefinite programs to model concrete applied problems or study deep problems in theoretical computational complexity.

A third breakthrough, with Aharon Ben-Tal, was the invention of robust optimization methods to address problems whose solutions may be very sensitive to problem data. Nemirovski also made seminal contributions to mathematical statistics, establishing the optimal rates at which one can recover certain classes of nonparametric signals from noisy data and investigating limits of performance for the estimation of nonlinear functionals from noisy measurements. His contributions have become bedrock standards with tremendous theoretical and practical impact on the field of continuous optimization and beyond.

Nemirovski earned his Ph.D. from Moscow State University in 1974. He has held research associate positions at the Moscow Research Institute for Automatic Equipment and the Central Economic Mathematical Institute of USSR/Russian Academy of Sciences, as well as a professorship at the Faculty of Industrial Engineering and Management, Technion, Israel. He has been a professor at the Georgia Institute of Technology’s H. Milton Stewart School of Industrial and Systems Engineering since 2005.

Nemirovski is a member of the U.S. National Academy of Engineering and the American Academy of Arts and Sciences. He is a recipient of the Fulkerson Prize of the Mathematical Optimization Society (MOS) and the AMS, the George B. Dantzig Prize of the MOS and SIAM, and the John von Neumann Theory Prize of the Institute for Operations Research and the Management Sciences.

“I am deeply honoured and grateful to receive the 2019 Norbert Wiener Prize — a distinction I never dreamt of,” Nemirovski said. “I have been fortunate to be taught by brilliant mathematicians at the Mechanical and Mathematical Faculty of Moscow University, where I was mentored by Georgi Shilov. I also had the honour and privilege of collaborating with outstanding colleagues like Yurii Nesterov, Aharon Ben-Tal, and Anatoli Louditski.”

“I always thought that the key word in ‘applied mathematics’ was ‘mathematics,’” he added. “Even when all we need at the end of the day is a number, I believe that what matters most are rigorous results on how fast this number can be found and how accurate it is, which poses challenging mathematical problems. I am happy to see how my research area—convex optimization—thrives due to the efforts of new generations of researchers, and how rapidly it extends the scope of its applications.”

For more details about the recipients of the 2019 Norbert Wiener Prize in Applied Mathematics, please view the Joint Mathematics Meetings 2019 prize booklet.