Brown Is Home to New NSF Math Institute

September 15, 2010

With a $15.5 million five-year award from the Division of Mathematical Sciences at the National Science Foundation, Brown University will create the Institute for Computational and Experimental Research in Mathematics. Joining such well-established counterparts as the IMA, IPAM, and MBI, ICERM brings the number of NSF-supported math institutes to eight.

Each of the institutes fills a particular niche. As this issue of SIAM News went to press, ICERM associate directors Jan Hesthaven and Bjorn Sandstede described ways in which activities of the new institute will be a good fit for the SIAM community. Jill Pipher, a professor of mathematics at Brown, is ICERM's director; along with Hesthaven and Sandstede, Jeffrey Brock, a professor of mathematics at Brown, is an associate director. Postdocs will play an important role in ICERM activities; applications will be solicited for the two one-year postdoc positions and eight semester postdoc fellowships that will be available each year.

The mission and focus of ICERM, Hesthaven and Sandstede explain, is to promote research at the interface between math and computers in the broadest sense. More specifically, institute programs will facilitate the use of computational methods in mathematics (from numerical computations to computer-aided proofs), promote the use of experimental methods in traditionally theoretical areas, and support theoretical advances related to computation or, more broadly, the use of computers in mathematical research. Some activities will emphasize ways in which computers can help mathematicians in nontraditional applications; others will focus on the use of mathematics to solve problems posed by the existence of computers---including large network problems, real-time search engines, large data, and many-sensor systems.

Asked to illustrate the experimental mathematics aspects of ICERM, Sandstede and Hesthaven were ready with examples, beginning with the famous Riemann hypothesis and the Hales proof of the Kepler sphere-packing hypothesis, the latter with its reliance on extensive and innovative use of computers. Another is the problem of finding closest points in high-dimensional lattices, and a final, more amusing example is the computer-aided proof that any combination on the Rubik's Cube can be solved in 20 or fewer moves. Each is a problem of deep mathematical complexity whose solution requires nontraditional and experimental combinations of math and computers.

ICERM will have two semester-long programs each year, along with summer activities for undergraduates and postdocs. The first two programs will be Kinetic Theory: Analysis and Computation, in the fall of 2011, and Complex and Arithmetic Dynamics, in the spring of 2012.

Interaction with industry is central to ICERM. The institute creators chose Google, Microsoft, and IBM as partners, in part because they are good matches thematically and in part because each has a very substantial math research group. Industrial input will help in shaping scientific programs; partners will identify mathematical problems from their industrial perspective. Industrial partners will also be involved in REU activities and in "Idea Labs," one-week "guided-teamwork" programs in which junior researchers will take on specific open problems.

Information about ICERM will be posted at http://icerm.brown.edu/ as it becomes available.



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