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 the fall, I will start a 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.

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 summer, I co-organized a Canadian Math Society Summer Meeting session on homotopy theory with Daniel Teixeira and Martin Frankland.

This spring, I co-organized the 4th Atlantic TQFT Spring School for grad students at Dalhousie University in Halifax, Nova Scotia.

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

• 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
• University of Illinois Urbana-Champaign Topology Seminar, Invertible Field Theories and the Bott Spiral - 3.31.26