Western math professor Chris Kapulkin earns national prize for applying topology to real-world challenges.
Western University’s Faculty of Science is celebrating an extraordinary achievement: Chris Kapulkin has been awarded the 2025 Coxeter-James Prize by the Canadian Mathematical Society. The national honour recognizes his groundbreaking contributions to topology and his applications of the mathematical field to real-world problems—from understanding complex data to ensuring software reliability.
Topology is the study of how shapes and spaces can be stretched or bent without breaking. “To a topologist, a coffee mug and a donut are the same thing,” he explained. “They both have one hole, so you can stretch or bend one into the other without breaking or ripping it.”
While the concept may sound abstract, Kapulkin’s work is grounded in real applications. He’s developing tools that apply these topological ideas to areas like data analysis and software verification. “We’re used to visualizing data as something that fits on a graph,” he said. “But real-world data—like weather, stock markets, or medical records—lives in many dimensions. It has shape. Our tools help detect those shapes.”
These shapes can reveal important patterns. Kapulkin gives the example of patient medical information. Each patient has tens or even hundreds of data points. If you simply use x and y coordinates to plot the data points, you will lose a lot of information. If there is a pattern or correlation between 6 of these data points, plotting these 6 data points may appear as a 6-dimensional shape. While we cannot visualize that shape, we can analyze it using mathematical tools. Plotting multiple data points simultaneously tells a better story of what is happening.
Another key part of Kapulkin’s work is formal verification—mathematically proving that software performs as expected. “When you e-transfer someone $20, you trust the software to work correctly,” he said. “Topology helps us build verification tools that can give us 100 per cent certainty. That’s essential in fields like banking, health care and transportation.”
The award also carries personal significance. The last Western recipient was John Frederick “Rick” Jardine in 1992, who was the department chair when Kapulkin was hired. Jardine was also a topologist. Kapulkin teaches Jardine’s theorem in one of his graduate courses—something that felt especially meaningful, as their careers followed similar paths from pure math to more applied problems. “It feels really special to continue that legacy,” he said.
Curiosity is at the heart of Kapulkin’s work. “I started as a pure mathematician who never thought about applications,” he said. “But my curiosity led me in this direction. The freedom to follow what interests me is one of the best parts of academic life.”
That curiosity continues to shape his research. Kapulkin is currently collaborating with the University of Florida’s Department of Medicine on a project exploring gene regulatory networks—systems that explain how genes interact with each other. They are applying the same topological techniques to understand how the human body functions.
What’s next? For Kapulkin, it’s about connecting with people who use the tools he develops. “I want to work with end users and make sure my research has real-world impact. That’s where it becomes meaningful.”
Whether it’s analyzing stock markets, supporting medical breakthroughs or ensuring the software we rely on works as intended, Kapulkin’s work is reshaping how we apply mathematics to the world around us. “We’re creating new tools that change the way we think about data,” he said. “And that’s incredibly exciting.”
