New math: A summer tradition expands to include non-Yale students

(Jeff Brock and David Dumas)

This summer, a popular Yale program that provides undergraduates with valuable mathematics research experience will undergo some intriguing addition of its own.

For the first time, the Summer Undergraduate Mathematics Research at Yale (SUMRY) program will be open to non-Yale undergraduates — a move that faculty advisors say will widen the program’s inclusion and diversity efforts and expand the pool of potential graduate students in math.

The expansion comes thanks to a three-year grant from the National Science Foundation.

SUMRY began at Yale in 2012 — although Yale has had some form of research experience program for undergraduates in math since the 1980s. Small groups of undergrads work with a faculty mentor on math projects that mix the rigor of high-level academic study with cutting-edge topics that mirror the leading research areas of today.

This year’s SUMRY cohort of 12 Yale undergrads and 12 non-Yale undergrads will begin the nine-week program — all virtual, due to the COVID-19 pandemic — on June 1.

Jeffrey Brock, dean of the School of Engineering & Applied Science, dean of science for the Faculty of Arts and Sciences, and the Zhao and Ji Professor of Mathematics, and Ian Adelstein, a lecturer in the Department of Mathematics, spoke with YaleNews about the program. Brock and Adelstein are co-directors of the program.

In broad terms, what is the value of the summer research program for undergraduates?

Brock: For many undergrads in mathematics, there’s a sense you’re climbing a really tall ladder just to where you can see the horizon. You don’t really get exposed to research problems in the traditional path until you are well into the process of graduate education. The thinking was that, if you can give undergraduates a taste of what it feels like to do mathematics research, that will give them some motivation to climb this ladder.

Adelstein: The program works hard to create an inclusive community over the summer; it’s important for students to experience mathematics in this environment. Unlike coursework and exams, which are often solitary experiences, the group-based nature of the program allows students to experience this collaborative aspect of learning and creating mathematics.

How is the SUMRY program structured?

Brock: There’s a senior mentor and a group of undergraduate students who work together. The problems presented to the group tend to be things at the frontier of research — new questions that aren’t known but can be approached with a little less up-front labor, where you’re looking at things that are easy to manipulate. A great example is “knot” theory. You’re studying closed loops in space and how they interrelate and how you can disentangle them. That’s a mathematical area that’s quite well developed, but you can approach problems at a simple level. Quite often, these small groups emerge with publishable results, under the careful guidance of a mentor.

This is a great way, to, first of all, get a taste of being a research mathematician. But it also gives undergraduates some exposure to the wider mathematical community, so when they’re applying to graduate school they may have some contacts outside of their own program.

Because this is a nine-week program, you really get to dig into a problem. The first couple of weeks are a review, with boot camp-style learning. The students meet with their mentor every day to gauge progress and do regular presentations to get a sense of what it’s like to give a mathematical talk.

Students on a Zoom meeting.
Students in the class on a Zoom meeting from last summer.

What was the motivation for expanding the program to include non-Yale undergraduates?

Brock: I think it brings a certain dynamism and cross-pollination that benefits everyone. You can bring people in with different perspectives and different academic backgrounds into the Yale mathematics ecosystem. It can be energizing.

It also allows us to think about potential recruiting possibilities for our graduate program, by looking at people who we might want to admit to our program and do it in a way that emphasizes inclusion.

Let’s delve deeper into that. How does SUMRY add to Yale’s efforts to expand inclusion and diversity in STEM fields?

Adelstein: The primary goal of the program is to engage a diverse group of undergraduate students in original mathematics research. We hope to build the diversity of the mathematics community by providing opportunities for women and underrepresented students at this early stage in their training.

This summer, thanks to the NSF support and a gift from the Dufault Fund at Yale, we are welcoming a class where over half of the students — and half of the project leaders — are women.

Who are the senior mentors for SUMRY?

Brock: Our research groups will be run by a range of faculty, both in and outside of the Department of Mathematics. One notable example is Smita Krishnaswamy [an associate professor of genetics and computer science], with whom we will be collaborating to run a program on geometric and topological data analysis. My hope is that this will become a signature component of SUMRY, in addition to more traditional areas in mathematics.

Adelstein: We know finding good mentors is an important aspect of continuing one’s training in mathematics. We recruited an incredibly diverse group of senior personnel for the NSF grant. Senior personnel and Yale faculty will mentor research groups over the three years of the grant. All of the senior personnel are women or from underrepresented groups — or both. All but two are from institutions other than Yale.

How did each of you get involved in the program? Why is it meaningful to you, personally?

Brock: I can speak from my own experience as a Yale undergraduate. I was close to considering other majors, just because I wasn’t sure what math was going to be like. It was the experience of a summer research program that exposed me to problems I could wrap my head around and solve — and it resulted in published papers that are some of my most-cited papers.

It was also my first experience of doing group research in mathematics, which is not commonly understood about mathematical work. We have this sort of mythology of the solitary genius and yet most of my papers have been coauthored with multiple authors. That experience of working with a group and having a long collaboration where you get together periodically, that social dimension is what propelled me to think, OK, this is a career I could really enjoy.

Adelstein: I really enjoy sharing my love of mathematics with the SUMRY students. It’s sometimes hard, though not impossible, to communicate the beauty of mathematics to a calculus class where many students are just fulfilling a requirement. By the time students are participating in a math research program, they are eager for all the insight and perspective you can provide, making for enjoyable and productive collaborations. My work with the SUMRY students is one of the most rewarding parts of my job at Yale.

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