Reposted from College of Science.

Understanding the intersection of mathematics, physics, biology and environmental science often requires stepping outside of the classroom and into the natural world. For University of Utah mathematicians Jody Reimer and Ken Golden, this entails venturing out into the Arctic where they study how the physical environment affects life in and on sea ice with the help of mathematical models.

In May 2024, Golden and Reimer led a field research trip to the coastal village of Utqiaġvik, Alaska, 300 miles north of the Arctic Circle. Though a fairly regular excursion, especially for Golden who has been to Earth’s frozen poles 19 times, this voyage was special. The researchers were accompanied by seven Utah students ranging from a high schooler to Ph.D. candidates seeking invaluable hands-on experience in the unique and extreme conditions of the Arctic ecosystem. The expedition was an opportunity to test mathematical models and field techniques and a rare chance for students to deepen their understanding of polar research.

Reimer, an assistant professor of both mathematics and biology, has studied how polar bear and seal populations respond to changes in sea ice as the climate warms. She has now turned her focus on the microbes that inhabit the ice itself and the adaptations that enable them to survive in such a harsh environment. Golden’s research examines complex multiscale physical properties of sea ice, from modeling ice floe dynamics at the macro-level down to calculating the porosity and permeability of the microscale brine inclusions seen in the ice. Together, Reimer and Golden are exploring the interplay between physics and biology, which turns out to be full of scientific surprises.

This interplay goes far deeper than one might expect, as Golden draws connections from astrobiology to military stealth technology and much in between.

“The math doesn’t care! It cross-pollinates all over the place,” he exclaimed. “The same mathematics we use to analyze how algae get nutrients from the brine phase can be used to monitor the onset and progress of osteoporosis in human bone!”

A trip to the Arctic tests mathematical models

This interdisciplinary work illustrates why mathematics is so critical for advancing science. It discovers patterns and correlations that ripple across the scientific spectrum, providing the best tools to make breakthroughs.

The 2024 outing was the largest field team ever led by Golden, and Reimer’s first time leading a field research expedition. Organizing the trip proved to be both a complex task and a valuable learning experience. There was the logistical planning and coordination with university legal teams since students were being introduced to harsh conditions which necessitated every safety protocol possible. The group also needed to acquire land use permits from the local Iñupiat groups of indigenous peoples. Students played a hands-on role in this process, packing equipment and troubleshooting issues in the field. The Barrow Arctic Research Center, where the students analyzed their ice samples, provided accommodations and logistical support.

Moving so much equipment across the ice had to be done carefully, especially in the presence of polar bears. Once in the field, these young mathematicians braved the Arctic cold in springtime — wind chill dropped to as low as 20 degrees below zero Fahrenheit on their first day — to conduct experiments linking mathematical models to real-world observations.

The Utah students on the trip included high school senior Anthony Lee, now a student at Stanford University; undergraduates David Gluckman, Kathy Lin and Nash Ward; and graduate students Daniel Hallman, Delaney Mosier and Anthony James.

Watching math students immerse themselves in field research was one of Reimer’s favorite parts of the trip. 

“Mathematics isn’t relegated to the realm of puzzles and isolated problems,” she said. “There’s fundamental and deep connections that affect all regions of life.”

The dance between modeling and field observations

Research like this demonstrates the value of interdisciplinary approaches in advancing applied mathematics. This integration is especially relevant in the modern day with the advanced technology that was a major component of this trip where new programs and equipment could be tested. One highlight was a device called a PlanktoScope, an open-source and portable imaging device that allows researchers to analyze microbial life in sea ice samples.

More affordable than traditional flow microscopy equipment, this tool enables broader access to high-quality image data collection. In Reimer’s lab, she and her students have since been analyzing the living organisms in the frozen samples they brought back. Some of these scientists are taking that technological integration a step further, processing the resulting images using AI-based tools that help sort and analyze thousands of microscopic snapshots of life hidden in the ice.

The trip illustrated the value of hands-on fieldwork in mathematical research. Measurements that were collected align with the existing literature and will serve as pilot data for future projects and funding proposals. By blending mathematical modeling with empirical observation, students and faculty gain insights into complex environmental systems.

Golden and Reimer have been analyzing the data they collected in the Arctic for more than year and are now planning the next expedition.

“We’re laying the groundwork for a broader suite of physical measurements, and ramping up on the biological side of things,” Golden said. This expands on their findings and further explores the intricate relationships between ice, living beings and the rapidly changing polar marine environment.

Funding for this expedition was provided by the National Science Foundation through the Applied Math Research Training Grant. The agency provided funding for two trips with the second planned for next year. And thanks to the work completed so far, this follow-up expedition is shaping up to be something truly special.

This is the cover story of Aftermath, the official publication of the Department of Mathematics at the University of Utah. Banner photo: Utah students collect ice cores on sea ice in the Arctic Ocean. 

• Brian Maffly Science writer, University of Utah Communications
  801-573-2382 brian.maffly@utah.edu