Chris Kapulkin

	Associate Professor	Email: kkapulki 'at' uwo.ca
	Department of Mathematics
	University of Western Ontario	Middlesex College 255C

Research

Interests

Homotopy Theory and (Higher) Category Theory
Applied Topology, including Topological Data Analysis
Formalization of Mathematics, including Homotopy Type Theory
Combinatorics, Graph Theory, and Network Analysis
Cryptography and Information Security

Selected publications

Data analysis using discrete cubical homology, with N. Kershaw, preprint, 2025. [arXiv]
Cubical setting for discrete homotopy theory, revisited, with D. Carranza, Compos. Math. 160, no. 12 (2024), 2856–2903. [arXiv] [CM]
Cubical models of (∞,1)-categories, with B. Doherty, Z. Lindsey, and C. Sattler, Mem. Amer. Math. Soc. 297 (2024), no. 1484, v+110 pp. [arXiv] [MAMS]
The Simplicial Model of Univalent Foundations (after Voevodsky), with P. LeF. Lumsdaine, J. Eur. Math. Soc. (JEMS) 23 (2021), no. 6, 2071-2126. [arXiv] [JEMS]
A Cubical Approach to Straightening, with V. Voevodsky, J. Topol. 13 (4), 1682-1700, 2020. [pdf] [J.Topol.]
Univalent categories and the Rezk completion, with B. Ahrens and M. Shulman, Math. Structures Comput. Science 25 (2015), no. 5, 1010–1039. [arXiv] [MSCS]

Complete publication list

Notes, videos, etc.

Upcoming talks and events

Speaker in the Mathematics Colloquium, University of Michigan, Ann Arbor, Mich., January 27, 2026.
Speaker in the Mathematics Colloquium, McMaster University, Hamilton, Ont., February 6, 2026.
Florence Bucke Prize Lecture, University of Western Ontario, London, Ont., February 11, 2026.
Speaker in the Mathematics Colloquium, University of Pittsburgh, Pittsburgh, Pa., March 27, 2026.
Invited speaker at the workshop Modularity of biological systems, National Institute for Theory and Mathematics in Biology, Chicago, Ill., April 13-17, 2026.
Speaker in the Geometry & Topology Seminar, University of Regina, Regina, Sask., May 2026.
Lead organizer (w/ D. Christensen, P. Goerss, and M. Robertson) of the Conference on Homotopy Theory, K-theory, and Topological Data Analysis (in honor of Rick Jardine), London, Ont., June 8-12, 2026.
Mini-course speaker (topic: ∞-categories) at the Summer School on Homotopy Colimits, University of Regina, Sask., June 22-26, 2026.
Invited speaker at the workshop Homology and homotopy in the world of graphs, EPFL Bernoulli Center, Lausanne, Switzerland, September 14-18, 2026.

Honours

Awards and fellowships

Coxeter-James Prize, Canadian Mathematical Society, 2025.
Florence Bucke Science Prize, University of Western Ontario, 2024.
Distiguished Research Professorship, Faculty of Science, University of Western Ontario, 2022-23.
Interdisciplinary Postdoctoral Fellowship (project: Cryptographic Multilinear Maps), University of Western Ontario, 2016-17.
Thomas C. Hales Distinguished Research Award, Department of Mathematics, University of Pittsburgh, 2014.
Andrew Mellon Predoctoral Fellowship, University of Pittsburgh, 2013-14.

Visiting positions

Research member, Mathematical Sciences Research Institute, Berkeley, Calif., 2022-23.
Research member, MSRI Higher Categories and Categorification Reunion Event, MSRI/Universidad Nacional Autónoma de México, Cuernavaca, Mexico, Summer 2022.
Research Member (program: Higher Categories and Categorification), Mathematical Sciences Research Institute, Berkeley, Calif., Spring 2020.
Fellow (program: Homotopy Type Theory and Univalent Foundations), Center for Advanced Study, Norwegian Academy of Science and Letters, Oslo, Norway, Fall 2018.
Participant (program: Big Proof), Isaac Newton Institute for Mathematical Sciences, Cambridge, U.K., Summer 2017.
Visiting student, Institute for Advanced Study, Princeton, N.J., 2012-13.

Supervision

Current students and postdocs

Diego Manco Berrio, postdoc, 2024-present.
Benjamin Connors, PhD student, 2023-present.
Nathan Kershaw, PhD student (Direct Entry), 2023-present.
Yufeng Li, PhD student (Computer Science, Cambridge, co-supervisor), 2023-present.
Maximilian Petrowitsch, PhD student (Philosophy), 2022-present.
Zack Dooley, PhD student, 2024-present. Previously MSc student, 2023-24.
Benni Ngo, PhD student, 2025-present.
Adrien Grenier, PhD student (Direct Entry), 2025-present.
Jacob Ender, MSc student, 2025-present.
Kyle Koyanagi, MSc student (co-supervisor), 2025-present.
Jeffrey Li, MSc student, 2025-present.

Supervision information

Teaching

Academic year 2025-26

Mathematics 9152B: Algebraic Topology II, Winter 2026.
Mathematics 3152B: Combinatorial Mathematics, Winter 2026.

Teaching information

Recommendation letters

Editorships

Associate Editor of the Canadian Journal of Mathematics.
Associate Editor of the Canadian Mathematical Bulletin.
Member of the Scientific Advisory Board at the Banff International Research Station.
Member of the Equity, Diversity, and Inclusion Advisory Board at the Banff International Research Station.
Editor of the special issue of Mathematical Structures in Computer Science dedicated to Marek Zawadowski (1960-2024).

Service

Present

Faculty sponsor of the student chapter of Association for Women in Mathematics at Western University.
Co-founder and organizer (j/w C. Angiuli, D. Christensen, and E. Riehl) of the HoTT Electronic Seminar Talks.
Organizer (j/w A. Medina-Mardones) of the Geometry/Topology Seminar at Western.
Co-founder and faculty advisor to the organizers (A. Chitan, M. James, M. Martin) of the Directed Reading Program at Western.

Past

Supervisor (j/w D. Carranza) in the 2025 Fields Undergraduate Summer Research Program (project 09: Formal verification of topological combinatorics), Fields Institute's outpost at Western University, Summer 2025.
Lead organizer (j/w A. Dochtermann and A. Rieser) of the Special Session on Discrete Homotopy Theory during the Mathematical Congress of the Americas 2025, Miami, Fla., July 21-25, 2025.
Associate Chair (Graduate), Department of Mathematics, Univeristy of Western Ontario, 2019-25.
Organizer (j/w B. Benedetti, A. Dochtermann, G. Paolini, and A. Rieser) of the Special Session on Discrete and Combinatorial Homotopy, Theory and Practice during the 2nd Joint Meeting of the Unione Matematica Italiana and the American Mathematical Society, July 23-26, 2024.
Lead organizer (j/w A. Dochtermann and A. Rieser) of the Special Session on Discrete Homotopy Theory during the Joint Mathematics Meetings 2024, San Francisco, Calif., January 3-6, 2024.
Lead organizer (j/w J. Beardsley, T. Brazelton, and D. Dugger) of the Special Session on Homotopy Theory during the Joint Mathematics Meetings 2024, San Francisco, Calif., January 3-6, 2024.
Organizer (j/w M. Frankland) of the Special Session on Homotopy Theory during the CMS Winter Meeting 2023, Montreal, Que., December 1-4, 2023.
Organizer (j/w C. Angiuli, D. Christensen, M. Hötzel Escardó, D. Licata, E. Riehl, and E. Rijke) of the HoTTEST Summer School 2022, online event, July-August 2022.
Organizer (j/w B. Ahrens, E. Cavallo, and A. Petkovic) of the HoTT/UF Workshop 2022, Haifa, Israel, July 31-August 1, 2022.
Organizer (j/w B. Ahrens) of the HoTT/UF Workshop 2021, The Internet @ Buenos Aires, Argentina, July 17-18, 2021.
Organizer (j/w B. Ahrens) of the HoTT/UF Workshop 2020, Paris (France) The Internet, July 5-7, 2020.
Organizer (j/w D. Christensen) of the HoTTEST Conference of 2020, only online, June 15-19, 2020.
Lead organizer of the conference From the Fundamental Lemma to Discrete Geometry, to Formal Verification (in honor of Thomas C. Hales on the occasion of his 60th birthday), University of Pittsburgh, June 18-22, 2018.
Organizer of the inaugural Midwest HoTT Seminar, May 26-27, 2018.
Organizer of Workshop and School on Univalent Mathematics, Birmingham, UK, December 11-15, 2017.
Program Committee member of the HoTT/UF Workshop 2017, 2018, 2019.
Lead organizer of the AMS Math Research Communities Workshop on Homotopy Type Theory, June 4-10, 2017.
Organizer of the Workshop on Homotopy Type Theory and Univalent Foundations, Fields Institute, May 16-20, 2016.