Impact: Research at Brown

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Brown's ICERM reimagines what mathematics can be

By Kevin Stacey and Noel Rubinton for IMPACT: Research at Brown

The Institute for Computational and Experimental Research in Mathematics — one of just six U.S. mathematical institutes — takes novel approaches in discovery, research and presentation.

PROVIDENCE, R.I. [Brown University] — Changing the way mathematicians approach their work has been the driving ambition of Brown’s Institute for Computational and Experimental Research in Mathematics (ICERM) since its start in 2010 as a national mathematics institute.

In July 2020, ICERM received a huge validation of its work, as the National Science Foundation made its largest award ever to Brown, giving the university and ICERM $23.7 million for the next five years of research and education programming.

ICERM’s Illustrating Mathematics program in the fall of 2019 certainly fit the institute’s goals, as it brought together dozens of mathematicians from around the world and also painters, sculptors and other visual artists to explore the images and objects produced in the course of mathematical study.

For three months, ICERM, high atop 121 South Main St. in Providence, buzzed with energy and overflowed with artwork during many in-depth sessions aimed at helping mathematicians use modern computer visualization in their research, using lectures, workshops and smaller-scale conversations that are a central part of the institute’s collaborations.

Panel discussions, many including professors from the Rhode Island School of Design, focused on the intersection of art and science, and a 3D printer brought in specially for the program rarely rested. Brown’s Granoff Center for the Creative Arts hosted a public exhibition of art created by mathematicians, and ICERM published its first-ever catalogue of mathematical art work. “We aim to show people that math is everywhere and intertwined with many branches of creative work,” said Brendan Hassett, ICERM's director and a mathematics professor at Brown.

Speaking about the NSF renewal grant, Hassett said, “Since its founding a decade ago, ICERM has been on a trajectory of steady growth in the research programs we offer and in the number of scholars and students who participate in them. We’re thrilled that NSF has recognized that trajectory and has chosen to renew our funding at such a high level.”

Jill Pipher, ICERM’s founding director and now vice president for research at Brown, said, “The funding level is a testament to the confidence that the National Science Foundation has in ICERM’s mission and in our execution of it. It is also a vote of confidence in the successful management of this major national research center, something that can only be achieved with the unwavering support from both faculty and administration that ICERM has enjoyed from its start in 2010.”

We aim to show people that math is everywhere and intertwined with many branches of creative work.

Brendan Hassett ICERM Director and Professor of Mathematics

With hundreds of mathematicians visiting each year, ICERM helps them share new ideas and collaborate on research projects. “A lot of people probably assume that what mathematicians do all day is work on computers and try to do hard computations,” Hassett said. “But the traditional approach to math is really pencil and paper. ICERM was founded on the need to focus on the aspects of mathematical discovery that involve playing with examples and doing experiments, which aren’t traditionally reported in mathematics scholarship.”

The power of that computational approach can be seen in ICERM’s contributions to major areas of mathematical research, Hassett said.

A recent example was ICERM-supported research on the Langlands program, a set of conjectures often viewed as a grand unifying theory of mathematics. ICERM’s work on the topic contributed to the L-Functions and Modular Forms Database — a collection of mathematical objects relevant to the Langlands program. The database now contains millions of objects and countless links between them.

“Our goal as an institution is to have an impact nationally on the mathematics culture, and that naturally enriches the mathematical and intellectual community at Brown,” Hassett said. “ICERM creates new opportunities for Brown faculty and students and fosters collaborations and interactions.”

Hassett said ICERM will continue to expand its programming. Among the activities already planned is a semester program on partial differential equations, the equations used to describe everything from fluid flows to gravitation. Another program will explore braids, the study of how strands of rope can be entangled. Braids give rise to algebraic structures that could be useful in data encryption.

ICERM will also focus on emerging venues for disseminating research findings and approaches. “The main vehicle for presenting scholarly output has traditionally been through academic journals,” Hassett said. “But, if a researcher is developing new computer code, a journal article isn’t always the best way to present it. We’re looking to expand the use and visibility of things like code repositories as a means of sharing new algorithms, approaches, and results.”

Another priority will be to expand outreach activities aimed at increasing diversity and inclusion in the mathematical sciences. Those activities include GirlsGetMath, a summer math camp for high school students held at ICERM. ICERM recently won a new grant from Jet Blue to take the program nationwide.

As in Illustrating Mathematics, ICERM, one of six federally funded mathematics institutes, brings new technologies and techniques to studying topics spanning pure and applied mathematics.

Pipher said she looks forward to seeing ICERM continue to flourish: “The quantity and quality of science and research being produced at this institute is just phenomenal.”

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