Education
University of Pittsburgh, Ph.D. in Mathematics
About
Chris Kapulkin is Professor of Computer Science and Mathematics at Vanderbilt University. His research spans a broad range of areas, including topics in pure mathematics (topology, category theory, and logic) and their applications in data analysis, computation, and the sciences.
He is best known for his work on the mathematical foundations of homotopy type theory, where he settled, jointly with Christian Sattler, the homotopy canonicity conjecture of Fields medalist Vladimir Voevodsky. He pioneered the program of relating type theory to higher category theory and developed cubical models of higher categories. With Daniel Carranza he proved the conjecture of Babson, Barcelo, de Longueville, and Laubenbacher on the topological realization of discrete homotopy groups, and has since built that result into a broad program spanning abstract homotopy theory, combinatorics, computation, and data analysis. His work has appeared in the Journal of the European Mathematical Society, Compositio Mathematica, and Memoirs of the American Mathematical Society.
He received the 2025 Coxeter–James Prize from the Canadian Mathematical Society, awarded for outstanding research contributions by an early-career mathematician, along with the 2024 Florence Bucke Science Prize and a Distinguished Research Professorship at the University of Western Ontario. He has been a research member at MSRI/SLMath and a fellow at the Center for Advanced Study in Oslo. He serves as an associate editor of the Canadian Journal of Mathematics and the Canadian Mathematical Bulletin, and sits on the Scientific Advisory Board of the Banff International Research Station.
Before joining Vanderbilt, he spent twelve years at the University of Western Ontario, where he was also graduate chair. He earned his Ph.D. from the University of Pittsburgh in 2014; his thesis resolved a conjecture of André Joyal and received the Thomas C. Hales Distinguished Research Award.
Research Focus
applied topology, formal verification, AI + Math
Publication Highlight
1. RedZeD: Computing persistent homology by Reduction to Zero Differentials, with N. Kershaw
2. The simplicial model of Univalent Foundations (after Voevodsky), with P. LeFanu Lumsdaine, J. Eur. Math. Soc. (JEMS) 23 (2021), no. 6, 2071-2126.
3. Cubical setting for discrete homotopy theory, revisited, with D. Carranza, Compos. Math. 160, no. 12 (2024), 2856–2903.