Polar adventures in math

Ask Ken Golden and Jody Reimer if a career in mathematics holds any adventure and they’ll tell you about dozens of trips to the Arctic and the Antarctic facing the cold, ice, roaring winds, engine room fires and, yes, polar bears.

Those aren’t the typical things that come to mind when you think of math professors, but Golden, a distinguished professor of mathematics, and Reimer, Wylie assistant professor of mathematics, are using the tools of mathematics to understand how the polar regions are changing as the world warms. Recently, their work was featured by BBC StoryWorks and the International Science Council in a web series called “Unlocking Science.” The series features 17 stories about how “scientists around the world are laying foundations to tackle major issues like climate change while creating inclusive, flourishing societies,” according to the series website.

Read the story, titled “Counting on mathematicians to help save the planet,” here.

Recently, Golden and Reimer spoke with Peter Trapa, dean of the College of Science, about this BBC StoryWorks story. They also talked about their research efforts and the College of Science’s ACCESS program, which provides a “signature first-year experience” for women enrolling in the college’s majors.

A transcript of their conversation follows, edited for length and clarity. Find the full discussion here.

Peter Trapa: 

Hi, my name is Peter Trapa. I’m dean of the College of Science here at the University of Utah. I’m joined by two of my very favorite colleagues, Ken Golden, Distinguished Professor of Mathematics and Jody Reimer, Wylie Assistant Professor of Mathematics.

But Ken and Jody are not at your traditional mathematicians. Collectively they’ve participated in 26 polar expeditions. Ken, why don’t you lead off by telling us a little bit about how this opportunity with the BBC arose?

Ken Golden:

Back in March, I was contacted by ICIAM, the International Council of Industrial and Applied Mathematics. And they told me that they had been contacted by the BBC to produce series of stories to showcase the role that science can play in solving some of society’s greatest collective challenges. And they felt, as do I, that math should have a seat at that table. And so I was asked to write a story to begin the selection process, which might help mathematics to be represented in the series. It’s been such a pleasure working with the BBC. You hear about the BBC being great professionals and boy, that’s what you find. So it’s been quite a great experience.


Can you tell us a little bit more about why it’s important to create awareness about how math is contributing to research around environmental science and environmental issues?


Well, if we make the public more aware of these things, then the public has a much better understanding of what math is, what math can do, what mathematicians actually work on and so on. And perhaps more importantly, it’s important that the public realize that math is not just some obscure field that is just taught in books or is practiced by just a very small corner of science. But in fact, math plays a central role in trying to solve some of society’s greatest problems, such as understanding and predicting what may happen to our climate system.

And moreover, by showing that math can address these kinds of large-scale problems of great societal interest, it naturally draws more people into mathematics. That’s what we need is we need more types of great minds to solve these very complex problems. And that’s one of the things we’re really trying to do, is to draw a much broader range of people into mathematics and science in general.


Yeah. Well, I couldn’t agree with you more, but of course I’m a mathematician myself, so you’re preaching to the choir here. So Jody, I want to turn to you. What brought you here to Utah to work with Ken and where do you see your research taking you from here?

Jody Reimer:

I had the amazing opportunity to do a PhD focused on using mathematical models to understand changes in polar bears and seals. I think you couldn’t ask for a kind of more interesting PhD project.

But while I was working on that, I became really fascinated by the bottom of that food web, what’s happening in the lower levels with the algae and the other primary producers in the Arctic. A really interesting study came out couple of years ago, showing that 70% of a polar bear’s diet, roughly, can be traced back to algae that grow inside the ice itself. And so I thought, well, if we’re going to understand Arctic change we need to understand not only sort of the big animals, but also what’s happening at the bottom.

And so when I left that position and was looking for my next one, I started looking around for which groups are doing really exciting work, combining mathematics and kind of polar research, especially with a strong focus on the sea ice, because understanding the ice is so important for understanding the things that live on and inside the ice.

And so Ken’s group was a very natural fit. There’s not a lot of mathematicians with a strong interest in the Arctic, especially with polar experience. And so I was thrilled to come here and join the strong group already here working on kind of the physics of these question and to pull in more of a biological component.


That’s really interesting. And I think what you’ve just said there speaks to the really highly interdisciplinary nature of your work, spanning everything from traditional mathematics and physics, all the way to ecological systems that you were just describing. So when you think in terms of interdisciplinary teams and drawing together all those different disciplines together, who have the two of you been working with here in Utah?


I’ve been deeply involved in the mathematics and materials groups for almost 30 years now, since I first got here, building that group up, which is an amazing group. And so our initial work on sea ice fit most naturally into that area.

However, with Jody coming here and with her great interest in this crossover and combining the basic mathematics of the microstructure of sea ice with the biology and the critters that live in there, that’s really brought a substantive deep connection with math biology. But also she’s been bringing in questions of uncertainty quantification, and incredible amounts of data and so on. And that’s made deep connections with our newly forming data science and machine learning groups, such as Akil Narayan and Bao Wang who are then connected to the Scientific Computing and Imaging Institute (SCI).

We’ve had a longstanding connection with atmospheric sciences and now with biology. One of the really interesting things about our work is that our studies of sea ice have led to very interesting results in the theory of composite materials and new kinds of exotic materials that have all kinds of fascinating behavior, and that has strengthened our ties with the physics department.


Yeah, that’s really impressive. And you think about addressing the grand challenges facing us, whether that’s climate change solutions or these other domains of extreme importance. You really have to weave all these threads together in the way that you just described. So Ken, why don’t we pivot a little bit and tell me a little bit about your involvement with the ACCESS program in the College of Science and what your ACCESS students get from doing research in mathematics?


Our ACCESS students get to experience somebody like Jody through her guest lectures and see how mathematics is part of a much broader picture of studying climate change and what polar bears are doing and how they’re affected by climate change and how we mathematically model some of these very important processes.

I knew Tanya Vickers, who’s our great director of ACCESS, who introduced me to some of our fantastic high school students many, many years ago, and got them started in research. And so I started mentoring some of our ACCESS students several years ago and, yes, lecturing in ACCESS. But then with an overall redesign of the ACCESS program, Tanya asked me to leave that for the Math Week component.

And so we focused on mathematics, climate and energy with an underlying theme of fractals. A pure math professor, Jon Chaika, has led the more pure math approach, and has also shown very clearly how pure and applied mathematics go hand in hand. Once we’ve really focused the attention of our ACCESS students onto this broader picture in how mathematics plays a central role in solving these larger problems like climate change, we’ve seen a dramatic increase in interest among our ACCESS students in doing math majors, as well as doing their research placements in the math department.

And I have to say one of the things that has been most exciting for me is, as you know Peter, I very often teach big introductory calculus classes, which I love. And this fall I’m teaching Calculus 3, multivariable calculus, which typically doesn’t have too many freshmen or first-year students in it. However, this year have 180 students and we have seven of our ACCESS students taking calculus 3 and they’re doing very, very well.


Over the years Ken has taught thousands, tens of thousands of undergraduate calculus students. And it’s happened more than one time than I’ve been on a chairlift riding with someone and when I mention I’m a math professor, they say, “Oh, do you know Ken Golden? He’s a great teacher.” So, very gratifying, Ken.

Jody, maybe you and Ken both can tell us a little bit about future opportunities for your research and what future students will be involved with?


Ken and I are both really excited about getting more students who are interested in mathematics into the field, ideally in an Arctic or Antarctic context. So hopefully some fieldwork in our future with students coming along to motivate them and also help them see the connection between the real-world setting, the challenges with where the data come from, and the challenges of that work environment. And also to motivate new questions and get their curiosity going. My own research has really benefited from experiences out in the field.

For myself, we’ve just been here a couple of years now and we’ve just sort of started scratching the surface on some of the really fascinating connections between the physics of sea ice and a really deep understanding of the physics at all these different scales from the microscopic to the macroscopic. And I think there’s a lot more exciting work there to do, to link it to the biology also at those various scales, the biology of microbial systems up to regional and ecosystem dynamics.


I’ve spent my early career particularly at Utah working on the millimeter scale brine microstructure of sea ice. And the overall arc of my career has sort of been to take that knowledge that we’ve learned and sort of the mathematics of homogenization, and how do you understand the larger scale properties of sea ice from knowledge of this micro scale, which is terribly important also to the ecology and the biology as well.

But what we hope for more in the future, and I’m working on now, is taking these same mathematical ideas but applying them to larger scale types of problems, such as the propagation of electromagnetic waves or radar waves through the brine microstructure is very similar to the propagation of ocean waves through the sea ice pack, which is a composite material, a granular self-similar fractal structure.

And there’s so many types of problems like this such as we’re taking the small scale micro structural physics, and applying that to the geometry of melt ponds, which determines the long term melting rate. So there’s all this beautiful notion of crosspollination where we’re taking ideas from one area, but the underlying mathematics is the same, and they might seem unrelated, but in fact we can carry over the mathematical and theoretical physics ideas.

And another kind of area that we’re really getting into, especially with Bao and Akil is developing mathematical models to better take advantage of vast amounts of data, which we really have access to now. And so I think that’s also a very important future direction that we’re taking.


Every time I talk to you, Ken and Jody, I get excited about what you’re doing, because it is so exciting to take underlying basic principles and find them in really important and impactful applications that are totally unexpected, so that’s very exciting. And I think also listening to you talk, you also capture that what you do is not only intellectually stimulating, but it’s great fun and I certainly get that sense from you too. So if people could take one or two lessons from the story that’s now being run by the BBC, what do you hope it will be?


Mathematics isn’t relegated to the confines of puzzles or fun problems that you do in isolation from the rest of the world that are rewarding, but not kind of connected to anything else. There are these really fundamental and deep connections between all types of mathematics. It’s not one specific branch, but I think there’s a broad range of types of mathematics that come to bear on a broad range of problems in several other disciplines, biology, physics, climate science.


Math is playing such a critical, fundamental role in helping us to address these large societal problems and specifically how to better understand and improve our predictions of Earth’s climate system, as well as the ecosystems that are intimately related with this, particularly in the polar regions where we’re seeing the most rapid changes due to our warming planet. The takeaway is that math is playing a fundamental role in solving these issues.

But also the last takeaway is the message from this ACCESS program that here in the math department at Utah and the College of Science we’re really trying to address another fundamental issue, mainly diversity in STEM fields and trying to bring more diverse faculty and students to work in these fantastic areas and challenging problems. And that we’re really trying to develop a model that really works to make it much more diverse, which we think is an important goal. We need a broad range of minds and ways of thinking to solve these very fundamental, complex problems such as climate change.


Well, I think this is a great place to wrap up. It’s always such a pleasure talking to both of you, Ken and Jody, getting a window into the exciting things that you’re doing and your great plans for the future. Thank you both again.

If you’re interested in learning more about what’s happening in the College of Science here at the University of Utah, I encourage you to visit our website, science.utah.edu. Thank you.

Learn more about Golden’s polar experiences in his recent Frontiers of Science lecture. You can find that lecture, and an award-winning video produced by University Marketing and Communications, here.

Media Contacts

Cassie SlatteryDirector of special projects, College of Science
Office: 801-587-7061