I am a mathematician inspired by problems in physics, and I am currently an NSF postdoc at the Perimeter Institute for Theoretical Physics.

I'm 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.

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

Previously, I was a postdoc at Dalhousie University. I completed my PhD at MIT, my master's degree through Part III at the University of Cambridge, and my undergraduate degree at Harvard.

Papers

(Click the dropdowns for summaries and collaborators.)

• 9. [2605.00316] Unraveling the Bott spiral
• 8. [2601.18701] Hyperkähler bases for six rational bordism theories
• 7. [2410.10031] Weak topological phases in the presence of interactions
• 6. Equivariant Witt Complexes and Twisted Topological Hochschild Homology in Topology and its Applications, 2025
• 5. A Higher Spin Statistics Theorem for Invertible Quantum Field Theories in Communications in Mathematical Physics, 2025
• 4. Smith homomorphisms and Spin$^h$ structures in Proceedings of the American Mathematical Society, 2024
• 3. The Smith Fiber Sequence and Invertible Field Theories in Communications in Mathematical Physics, 2026
• 2. [2403.01651] Dagger $n$-categories
• 1. A Long Exact Sequence in Symmetry Breaking: order parameter constraints, defect anomaly-matching, and higher Berry phases in Journal of High Energy Physics, 2025

Other Writings

• [2509.10636] Higher tensor categories and their extensions: notes from the Scottish Talbot On Algebra and Topology

Invited Talks

• Quasicrystals in Fundamental Physics, ICMS Edinburgh, Free-to-Interacting Maps for Quasicrystalline Symmetry-Protected Topological Phases - 6.20.26
  • Slides
• Global Categorical Symmetries 2026 Conference, Institut Henri Poincare, Paris, France. Invertible Field Theories and the Bott Spiral - 6.23.26
• Canada Math Society Summer Meeting, Noncommutative Geometry and Applications Session, Twisted Atiyah--Bott--Shapiro Maps and SPTs - 6.7.26
• Canada Math Society Summer Meeting, Category Theory Session, Dagger Categories and Higher Spin Statistics - 6.7.26
• NYU Center for Quantum and Topological Systems (CQTS) Geometry and Topology Seminar, Invertible Field Theory Models for SPTs in the Bott Spiral - 4.8.26