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Computational and Applied Mathematics Initiative

An increasing interest in analyzing and modeling high-dimensional data, both static and dynamic, and handling very large data sets in multiple scientific domains has led to an increased flow of ideas between applied mathematics, statistics, and computation. A synergy is emerging among fields such as statistical modeling of high-dimensional data, parameter estimation, optimization, machine learning, dynamical systems, numerical methods, and computational mathematics. Examples can be found in the exciting recent progress in the genome sciences, where statistically based computation has become an intrinsic part of research in human genetics; in the growing interaction between spatial statistics and the numerical analysis of atmospheric and ocean dynamics data, driven in large part by extensive new data sets being acquired through satellite imaging; in the extensive use of statistical modeling and probabilistic analysis for data analysis and modeling in neuroscience. Another aspect of these developments is the rapid convergence of research interests between Statistics and Computer Science. The traditional computer sciences domain of Artificial Intelligence has, during the past decade, increasingly adopted statistical methods, to the point that, today, the two fields are entirely integrated.

The history of applied mathematics at the University of Chicago is filled with great names who have had major impact in analysis, PDE's, harmonic analysis, numerical methods, and statistics. Moreover, in the past decade the University has created the Computation Institute, which serves as a focal point for projects involving high-end and massively parallel computing. And yet we have not seen emerge a consistent program in computational and applied mathematics that is able to meet the challenges presented by these new developments, both in terms of research and in terms of graduate and undergraduate education. Given the strong interdisciplinary ties developed by faculty in the Department of Statistics with quite a number of scientific fields, and the ongoing emphasis on integrating theory and methodology with real problems and data, it seemed a natural home for developing such a program, which was formally initiated in 2008.

In the past several years we have hired a number of faculty with background and interests in a variety of domains involving computational and applied mathematics. Lek-Heng Lim is an applied mathematician studying numerical methods involving tensors and their application to large and high-dimensional data sets; John Reinitz is a mathematical biologist hired jointly with Ecology and Evolution; John Lafferty and Risi Kondor both work in machine learning and the analysis of high-dimensional data and were hired jointly with Computer Science; Nicolas Brunel is a computational neuroscientist hired jointly with Neurobiology; Mihai Anitescu is an applied mathematician working in numerical methods for PDE’s and optimization and is a joint hire with Argonne National Laboratory. Jonathan Weare is an applied mathematician working on stochastic simulation, in particular, simulation of rare events with applications in computational chemistry and geophysical sciences and is joint with the James Franck Institute. Mary Silber is an applied mathematician working on dynamical systems, most recently as tools to describe pattern formation in natural phenomena. Guillaume Bal who will join the department in summer 2017, is an applied mathematician working on inverse problems in PDE’s and mathematical models for hybrid imaging systems and will be joint with the Department of Mathematics.

These exciting new hires come in addition to many existing faculty in the Departments of Statistics, Mathematics, Computer Science, Physics, Astrophysics, Chemistry, and Geophysical Sciences, who are involved in various aspects of applied and computational mathematics. These faculty have now formed the core group of the new Committee on Computational and Applied Mathematics, a degree granting program that was approved by the University Senate in fall 2016.

Last update: 1/4/17