In the Point Configurations program, participants made the ICERM offices their base for more than three months, using spaces designed to encourage and support collaborations. From formal presentations to workshops, from spontaneously planned ad hoc programs to conversations over lunch, participants discussed current research questions and started new collaborations.

“One major impact of the program has been to strengthen the internal coherence of this widespread subject of growing importance, which intersects with geometry, analysis, physics, and computer science,” said Peter Grabner of Graz University of Technology in Austria, a member of the program’s organizing committee.

“New collaborations were formed that have already led to progress on such topics as lattice theory, packing, and statistical physics,” said the chair of the organizing committee, Edward Saff, a mathematics professor at Vanderbilt University. Communication among workshop participants is continuing, and a follow-up conference in two years is being considered, as is a new academic journal on the subject.

Leading scholars from around the world attended the program—a few months later, one of the workshop leaders, Akshay Venkatesh of the Institute of Advanced Study in Princeton, was awarded a Fields Medal, an award often described as the Nobel Prize of Mathematics.

A large goal of ICERM programs is to develop the next generation of top researchers. “The camaraderie among participants played an important role in the program’s success,” Saff said. “There were no lines of division between graduate students, postdoctoral students, and senior scientists.”

Enhancing the program was intense activity in the mathematical field about its subject in the months leading up to its start. Henry Cohn, a principal researcher for Microsoft Research New England who is also on the Scientific Advisory Board of ICERM, published widely noted research on sphere packing in 24 dimensions. His work was discussed both at ICERM and in a Distinguished Lecture series with him, hosted by the mathematics department at Brown and attended by faculty, undergraduates, and graduate students. The problem of two-dimensional sphere packing was solved in the mid-20th century by Lazlo Fejes Tóth, but it was not solved in three dimensions until Thomas Callister Hales did so in 1998, an accomplishment confirmed by computer check in 2014.

“Fundamental research in the mathematical sciences produces unexpected benefits,” said Jill Pipher, Brown’s vice president for research, and also founding director of ICERM and professor of mathematics. “The research that is pursued, simply because it pushes the frontiers of mathematical truth further, often pays dividends years and decades later in solving real-world problems,” she added.

For instance, she said, number theory, once thought to have no connection to the broader world, eventually led to a new paradigm in encryption and helped make the Internet age imaginable and digital financial transactions possible.

Though by design ICERM programs, which are supported by a five-year, $17.5M federal grant, involve far more visitors than Brown faculty and students, the impact on Brown is large. Dan Abramovich, a professor of mathematics and chair of mathematics, said, “An ICERM program floods Brown with a group of researchers in a particular topic. Our departments and other centers benefit from a supply of seminar and colloquium speakers, concentrated exposure to current research in a particular topic, and a general expansion of the Brown community, often keeping links well after the end of a program.”