The Richard N. Merkin Center for Pure and Applied Mathematics has now taken up residence on the 8th floor of Caltech Hall and is hosting the American Institute for Mathematics.

The American Institute of Mathematics (AIM) has been offering resources to mathematicians of all ages and stages since its founding in 1994. Previously located in San Jose, California, AIM now makes its home at Caltech, where it works hand in glove with the new Richard N. Merkin Center for Pure and Applied Mathematics to continue AIM's mission "to advance mathematical knowledge through collaboration, to broaden participation in the mathematical endeavor, and to increase the awareness of the contributions of the mathematical sciences to society."

AIM is one of seven National Science Foundation (NSF)-funded institutes for mathematics. Each of these institutes "has its own mission and types of mathematical programs," says Caltech's Sergei Gukov, John D. MacArthur Professor of Mathematics and Theoretical Physics and director of the Merkin Center. "AIM's signature dish," says Gukov, "is its unique workshop style that facilitates collaborations among mathematicians." It accomplishes this through three programs: workshops and SQuaREs (structured quartet research ensembles), which both meet in person on the Caltech campus, and online communities.

Workshops bring together 25–30 mathematicians who work in the same field to spend a week working on a particular set of mathematical problems. "It's very ambitious to try to prove a theorem in one week," says Gukov, "but as they say, shoot for the stars if you want to land on the moon. Even if the workshop participants don't prove major theorems by the end of the week, they at least have a project or collaboration going that they continue once they leave the workshop."

SQuaREs are smaller groups of around four mathematicians, usually from different institutes or universities, who come up with their own projects and work together in three one-week sessions at AIM over the course of three years.

AIM's online communities developed during the pandemic. Their topics are more general than those taken up in workshops and SQuaREs and include a larger and broader swath of mathematicians (40–150 people in total), including graduate students.

Beyond these initiatives, AIM sponsors special projects that bring financial and administrative resources and mathematical expertise to a number of other organizations, including MathCommunities, which serve pre K to 12th-grade students; MathCircles, for students and teachers of K–12 math; the Global Math Project, which is bringing new approaches to math in more than 150 countries worldwide; Math Monday, a lunchtime activity for grade-school students; the Alliance of Indigenous Math Circles, which sponsors math groups and math camps for indigenous students in Arizona, Utah, New Mexico, Oklahoma, and North Carolina; Research Experiences for Undergraduate Faculty (REUF) to help faculty at undergraduate institutions carry out math research and mentor their students; Mathematics of Planet Earth, an international collaboration of people interested in bringing mathematics and computational models to the earth sciences; and more.

AIM's scientific board, composed of 20 mathematicians with many different specializations, makes recommendations for potential topics and participants and selects which events, from many proposals, AIM will sponsor. Gukov was himself a participant in an AIM workshop before joining its scientific board, on which he served for many years. "Competition for workshop space is lively," says Gukov. "I've never seen a year when there were not enough quality proposals available. Usually our problem is having to say no to really wonderful proposals because there's just not enough room."

The growth of AIM projects and activities has led the institute to add several new staff members to manage special projects and to keep workshops running smoothly. Gukov is now heavily involved in helping AIM and its new and relocating staff to transition to their new home. Space will eventually be freed up in the W. K. Kellogg Radiation Laboratory to provide a more permanent home for AIM staff and visiting affiliates and AIM's extensive mathematics library of textbooks, monographs, and even some rare books. The Merkin Center will remain in continuous use for workshops and SQuaREs.

AIM is now running a different workshop every other week as well as 4–6 SQuaREs concurrently in alternate weeks. "People love this space, they're so happy here," says Michelle Manes, deputy director of AIM.

"The enthusiasm of our Caltech faculty was instrumental in getting this project off the ground and the efforts of Caltech staff, including Esperanza Madrigal, Shawna Silesky, Carol Silberstein, and Michelle Vine—who spent countless hours helping us on an almost daily basis—made the relocation of AIM as smooth as it could possibly be," Gukov says. "There are quite a few small things that need to be finished, but thanks to everyone's unparalleled help and support we are definitely off to a good start."

"We're delighted to have AIM on campus," says Caltech Provost David Tirrell. "Because our colleagues in mathematics have participated in AIM workshops and SQuaREs in the past, we were aware of the high quality and intellectual vitality of AIM programs and the extent to which they would complement and enrich the activities of our own math community. It's great to see that happening."

Caltech and the Division of Physics, Mathematics and Astronomy will be holding an open house for AIM on Tuesday, October 10, from 12:00 to 6:00 pm. There will be a reception and several welcome speeches on the lawn outside Caltech Hall and tours of the Merkin Center on the 8th floor.

Written by Cynthia Eller