Dr. Chris Kapulkin to receive the 2025 Coxeter-James Prize

Ottawa, ON – The Canadian Mathematical Society (CMS) is pleased to announce that Dr. Chris Kapulkin (Western University) is the recipient of the 2025 Coxeter-James Prize. Dr. Kapulkin works in homotopy theory, applying its techniques to numerous other areas of mathematics, including formal logic, theoretical computer science, combinatorics, category theory, and interactive theorem proving.

Dr. Kapulkin earned his Ph.D. in Mathematics from the University of Pittsburgh in 2014. He then joined the University of Western Ontario, initially as a Postdoctoral Fellow, and is now an Associate Professor with tenure. Since 2010, he has authored nearly 40 research papers.

Dr. Kapulkin is best known for his work in homotopy type theory, a field that connects homotopy theory with the foundations of mathematics, specifically type theory. In 2010, Dr. Voevodsky proposed the homotopy canonicity conjecture, which Dr. Kapulkin and Dr. Sattler later proved. This conjecture is important because it helps refine the way equality and equivalence are understood in foundations of mathematics. Homotopy type theory is widely used in proof assistant software, such as Lean, Agda, and Coq, which help mathematicians formally verify proofs. For his contribution, Dr. Kapulkin received the Florence Bucke Prize in Science in 2024.

Beyond this proof, Dr. Kapulkin has made significant contributions to the field. In his Ph.D. dissertation, he solved a problem posed by Dr. Joyal in 2011 about the structure of higher categories in type theory. His work introduced new techniques, such as using Brown’s fibration categories to interpret type theory, which have since become standard in the field. Collaborating with Dr. Peter LeFanu Lumsdaine, he extended Dr. Joyal’s ideas, proposing a system of three conjectures that link logical systems with higher-categorical structures. These conjectures have guided much research in homotopy type theory, though only the first has been proven so far (by Dr. Kapulkin himself, alongside Dr. Karol Szumiło in 2019).

Dr. Kapulkin has also led efforts in developing cubical models of higher categories. Traditionally, higher categories have been studied using simplicial sets, but this approach has limitations stemming from cumbersome formulas for products of simplices. To overcome these issues, Dr. Kapulkin and his collaborators introduced cubical models, which provide a more practical framework for handling structures involving iterated products of higher categories. Their work has influenced various areas of mathematics, including derived representation theory and differential geometry. Today, cubical models of higher categories have become an independent field, attracting researchers from around the world.

Another notable achievement of Dr. Kapulkin is his proof, with his student Daniel Carranza, of a major conjecture in topological combinatorics. This problem belongs to discrete homotopy theory, which assigns homotopy and homology groups to graphs, providing valuable combinatorial insights. A natural question is whether these homotopy and homology groups arise from a topological space that one can associate to a graph. In 2006, one such construction was proposed, but the desired property remained an open problem until 2022, when Dr. Kapulkin and Carranza proved it by introducing new techniques from cubical and abstract homotopy theory. This breakthrough has implications not only in pure mathematics, but also in applied fields like data analysis. His results, joint with his student Nathan Kershaw, have improved software calculations of network invariants and contributed to understanding gene regulatory networks, in collaboration with researchers at the University of Florida’s Department of Medicine.

Dr. Kapulkin’s contributions have been acknowledged through numerous awards and accolades, including the aforementioned Florence Bucke Science Prize (2024), a Faculty of Science Distinguished Research Professorship at Western University (2022-23), several recognitions on Western University’s Undergraduate Teaching Honor Roll, and the Thomas C. Hales Distinguished Research Award from the University of Pittsburgh (2014), among other honours.

Beyond his research contributions, Dr. Kapulkin plays an active role in the Canadian mathematical community. He is an associate editor for both the Canadian Journal of Mathematics and the Canadian Mathematical Bulletin, overseeing submissions in areas such as algebraic topology, category theory, cryptography, and the formalization of mathematics. Additionally, he serves on the CMS Equity, Diversity, and Inclusion (EDI) Committee and has contributed to CMS Notes. A regular participant in CMS meetings, he frequently contributes as a speaker and organizes special sessions. As one colleague noted,

“He is an amazing communicator of mathematics and adjusts perfectly to his audience, making even the deepest arguments from his work accessible to us higher category novices. It is a real pleasure to engage in mathematical discussions with him, and we have all benefited greatly from his expertise and ability to work across fields.”

Since 2023, Dr. Kapulkin has also been a member of both the Scientific Advisory Board and the EDI Advisory Board of the Banff International Research Station.

In summary, Dr. Chris Kapulkin’s groundbreaking contributions to homotopy theory and its applications, along with his dedication to the Canadian mathematical community, make him a truly deserving recipient of this prize. His influential research in the areas of category theory, type theory, and topological combinatorics, has shaped multiple fields and inspired ongoing work in mathematics and theoretical computer science. The CMS is proud to award Dr. Kapulkin with the 2025 Coxeter-James Prize and looks forward to his future contributions to mathematical research.

About the Coxeter-James Prize
The Coxeter-James Prize was inaugurated in 1978 to recognize young mathematicians who have made outstanding contributions to mathematical research. The award is named for two former CMS presidents, Donald Coxeter, who is recognized as one of the world’s best geometers, and Ralph Duncan James, who was a great contributor to mathematical development in Canada.

For more information, visit the Coxeter-James Prize page.

About the Canadian Mathematical Society (CMS)
The Canadian Mathematical Society (CMS) is the main national organization whose goal is to promote and advance the discovery, learning and application of mathematics. The Society’s activities cover the whole spectrum of mathematics including meetings, research publications, and the promotion of excellence in mathematics competitions that recognize outstanding student achievements. The CMS is a registered non-profit, charitable organization and depends on grants, funding, and generous donations from sponsors, benefactors and community members to be able to carry out its activities.

For more information, please contact:

Dr. Susan Cooper (uManitoba) Chair, CMS Research Committee Canadian Mathematical Society chair-resc@cms.math.ca

or

Dr. Termeh Kousha Executive Director Canadian Mathematical Society tkousha@cms.math.ca