Jeremy Quastel has been awarded NSERC’s John C. Polanyi Award. The award recognizes research that has led to a recent outstanding advance in natural sciences or engineering.
Quastel is recognized for his pioneering work in probability theory, particularly in advancing our understanding of randomness in nature. His research focuses on the Kardar-Parisi-Zhang (KPZ) fixed point, a recently constructed mathematical object that explains how seemingly unrelated random growth processes, such as coffee stains or bacterial colonies, share universal patterns.
Quastel’s breakthrough came from identifying and proving the existence of this fixed point. By demonstrating that numerous models, including the foundational KPZ equation, converge to it, he has unified several major areas of mathematical research. This achievement not only deepens our understanding of complex systems but also opens new pathways for innovation across disciplines such as physics, biology, and materials science.
Reflecting on the recognition, Quastel shared:
It's great that an NSERC prize for research in science has gone to mathematics this time, a recognition that Canada has really first-rate mathematics —and that the exact sciences, math, CS, stats, are becoming so much more important.
Quastel’s pioneering research has positioned the department as a global leader and continues to inspire a new generation of mathematicians. The department Chair praised Quastel’s work, noting:
Jeremy Quastel has made remarkable contributions to mathematics by uncovering deep patterns in how randomness behaves over time. His seminal work on the Kardar–Parisi–Zhang universality class culminated in the discovery of the KPZ fixed point, a breakthrough that reshaped the modern study of random growth models.
A short Q&A with Quastel:
What inspired you to study randomness and pursue research in probability theory?
When I was an undergraduate at McGill, we were taught abstract topics like category theory. I did a summer NSERC placement at UBC, where there was a strong group in probability, and their research seemed more connected to the kinds of scientific problems that appealed to me. They encouraged me to study at Courant, where there were some young superstars—Varadhan, Papanicolaou, and Spencer. With Varadhan—and later H.-T. Yau, who joined as a postdoc—we studied hydrodynamic limits: how equations like the heat and fluid equations arise from large interacting systems of particles. It sounds like partial differential equations, but it’s really based on probability.
My first job was at UC Davis in ’91, where Tracy was already there and Widom visited from Santa Cruz. They were discovering the limit laws for random matrix eigenvalues. It all came together later in KPZ, where the same limit laws appear and turn out to come from this famous integrable system, KP.
What potential applications of your research are you most excited about?
When I started working on KPZ, it wasn’t clear there was really something to it. It wasn’t making sense mathematically, and the physical phenomena weren’t convincingly observable. Now, every couple of weeks, I receive an article for Physical Review Letters where researchers claim to observe KPZ fluctuations in some physical system.
But I feel the most important aspect is that, in non-equilibrium statistical mechanics—where we still know so little—these are systems where, through the joint efforts of mathematicians and physicists, we’ve been able to make real progress.
What advice would you give to young mathematicians or researchers interested in pursuing theoretical work?
It's hard in mathematics to guess where one might be able to make advances. So, there's a natural tendency to stick to what one's been trained in, and many people do make great progress that way. But another way is to try different things that you think are important, but nobody's working on them. Maybe because people thought they were impossible. But you start from the beginning and see how far you can go.
Looking ahead, what questions or challenges in probability theory are you most eager to explore next?
There are all these mysteries in KPZ I can't stop thinking about. The big problem is universality—how to prove the analogue of the central limit theorem. In general, I hope to keep trying to develop methods to study the collective behavior of large interacting systems. For stochastic partial differential equations, they are used all over the place, but except for a few cases like KPZ, the most we can say now is they make sense. I'd like to try to find out what they actually do.