I am a mathematician inspired by problems in physics, and I am currently a Killam postdoctoral fellow at Dalhousie University in Halifax, Nova Scotia. In 2027, I will move to 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, quantum information, lattice models, 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.

Articles

• 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 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
• MIT Topology Seminar - Invertible Functorial Field Theory for Symmetry Breaking and Interactions in Quantum Field Theory - 4.28.25
• Harvard Center for Mathematical Sciences and Applications - Homotopical Methods for Free and Interacting Fermionic SPTs - 3.31.25
  • Video
• Homotopy Theory Special Session at the Joint Math Meetings 2025 in Seattle - Twisted Atiyah-Bott-Shapiro Maps - 1.11.25
  • Slides

More Invited Talks