I am a mathematician inspired by problems in physics, and I am currently a Killam postdoctoral fellow at Dalhousie University in Halifax, Nova Scotia. My next appointment will be at the Perimeter Institute for Theoretical Physics.

I'm particularly interested in topological phases of quantum matter and anomalies of quantum field theories. I like to think about topological $K$-theory, topological quantum field theory, dagger categories, quantum information, and equivariant algebra.

Previously, I completed my PhD at MIT, my master's degree through Part III at the University of Cambridge, and my undergraduate degree at Harvard. In high school, I attended Linden Hall School for Girls and participated in the Hampshire College Summer Studies in Mathematics.

My email is ckrulewski [at] dal [dot] ca.

Conferences

This spring, I am co-organizing the 4th Atlantic TQFT Spring School for grad students at Dalhousie University in Halifax, Nova Scotia. Interested students should apply before March 31, 2026.

Articles

• 10. [2605.00316] Unraveling the Bott spiral
• 9. [2601.18701] Hyperkähler bases for six rational bordism theories
• 8. [2509.10636] Higher tensor categories and their extensions: notes from the Scottish Talbot On Algebra and Topology
• 7. [2410.10031] Weak topological phases in the presence of interactions
• 6. [2409.05965] Equivariant Witt Complexes and Twisted Topological Hochschild Homology
• 5. [2408.03981] A Higher Spin Statistics Theorem for Invertible Quantum Field Theories
• 4. [2406.08237] Smith homomorphisms and Spin$^h$ structures
• 3. [2405.04649] The Smith Fiber Sequence of Invertible Field Theories
• 2. [2403.01651] Dagger $n$-categories
• 1. [2309.16749] A Long Exact Sequence in Symmetry Breaking: order parameter constraints, defect anomaly-matching, and higher Berry phases

Invited Talks

• University of Illinois Urbana-Champaign Topology Seminar, Invertible Field Theories and the Bott Spiral - 3.31.26
• University of Tokyo, Theoretical Studies of Topological Phases of Matter Conference - Free and Interacting Fermionic SPTs and the Bott Spiral - 12.2.25
• University of Edinburgh Algebra Seminar - Invertible Field Theories and the Bott Spiral - 11.5.25
• Isaac Newton Institute, Quantum Field Theory with Boundaries, Impurities, and Defects Pro- gram - Invertible Field Theories and a Long Exact Sequence in Symmetry Breaking - 11.4.25
• Atlantic Category Theory Seminar - Dagger Categories and Higher Spin Statistics - 10.7.25