outside the mathematical sciences. In this way, it has helped to nucleate new communities and networks in topics such as mathematical materials science, applied algebraic geometry, algebraic statistics, and topological methods in proteomics. The Institute for Pure and Applied Mathematics (IPAM) hosts a similar percentage of researchers from other disciplines.

The institutes have had success in initiating new areas of research. For example, IPAM worked for 9 years to nucleate and then nurture a new focused area of privacy research, starting with a workshop on contemporary methods in cryptography in 2002. That led to a 2010 workshop on statistical and learning-theoretic challenges in data privacy, which brought together data privacy and cryptography researchers to develop an approach to data privacy that is motivated and informed by developments in cryptography, one of them being mathematically rigorous concepts of data security. A second follow-on activity was a 2011 workshop on mathematics of information-theoretic cryptography, which saw algebraic geometers and computer scientists working on new approaches to cryptography based on the difficulty of compromising a large number of nodes on a network. Another IPAM example illustrates that the same process can be important and effective in building connections within the discipline. A topic called “expander graphs” builds on connections that have emerged among discrete subgroups of Lie groups, automorphic forms, and arithmetic on the one hand, and questions in discrete mathematics, combinatorics, and graph theory on the other. In 2004 IPAM held the workshop Automorphic Forms, Group Theory, and Graph Expansion, which was followed by a program on the subject at the Institute for Advanced Study in 2005 and a second IPAM workshop, Expanders in Pure and Applied Mathematics, in 2008. Similarly, the Statistical and Applied Mathematical Sciences Institute (SAMSI) has worked to develop the general topic of low-dimensional structure in a high-dimensional system. Many problems of modern statistics arise when the number of available variables is comparable with or larger than the number of independent data points (often referred to as the p > n problem). Traditional methods for dealing with such problems involve techniques such as variable selection, ridge regression, and principal components regression. Beginning in the 1990s, more modern methods such as lasso regression and wavelet thresholding were developed. These ideas have now been extended in numerous directions and have attracted the attention of researchers in computer science, applied mathematics, and statistics, in areas such as manifold learning, sparse modeling, and the detection of geometric structure. This is an area with great potential for interaction among statisticians, applied mathematicians, and computer scientists.

The Mathematical Sciences Research Institute (MSRI) is focused primarily on the development of fundamental mathematics, specifically in areas in which mathematical thinking can be applied in new ways. Programs

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