have spanned topics such as mathematical biology, theoretical and applied topology, mathematics of visual analysis, analytic and computational elliptic and parabolic equations, dynamical systems, geometric evolution equations, parallel computing for mathematics, computational finance, statistical computing, multiscale methods, climate change modeling, algebraic geometry, and advances in algebra and geometry.

In spite of its primary focus on the mathematical sciences per se, MSRI has long included a robust set of outreach activities. For example, its 2006 program Computational Aspects of Algebraic Topology explored ways in which the techniques of algebraic topology are being applied in various contexts related to data analysis, object recognition, discrete and computational geometry, combinatorics, algorithms, and distributed computing. That program included a workshop focused on application of topology in science and engineering, which brought together people working in problems ranging from protein docking, robotics, high-dimensional data sets, and sensor networks. In 2007, MSRI organized and sponsored the World Congress on Computational Finance, in London, which brought together both theoreticians and practitioners in the field to discuss its current problems. MSRI has also sponsored a series of colloquia to acquaint mathematicians with fundamental problems in biology. An example is the 2009 workshop jointly sponsored by MSRI and the Jackson Laboratories on the topic of mathematical genomics. Both MSRI and SAMSI have helped build bridges between statisticians and climate scientists through at least six programs focused on topics such as new methods of spatial statistics for climate change applications, data assimilation, analysis of climate models as computer experiments, chaotic dynamics, and statistical methods for combining ensembles of climate models.

IPAM and SAMSI provide two additional illustrations of how the institutes build new connections to other disciplines. After a professor of Scandinavian languages at UCLA participated in a 2007 IPAM program on knowledge and search engines, which introduced him to researchers and methods from modern information theory, he went on to organize two workshops in 2010 and 2011, on networks and network analysis for the humanities; the workshops were funded by the National Endowment for the Humanities and cosponsored by IPAM. They led to the exploration of new data analysis tools by many of the humanists who participated. SAMSI’s example comes from a more established area, the interaction between statistics and social sciences, which SAMSI has supported through several activities, such as a workshop to explore computational methods for causal modeling and for the analysis of transactions and social relationships.

The IMA has a long history of outreach to industry, for instance through its Industrial Postdoctoral Fellowship program and other activities

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