I am a mathematician inspired by problems in physics, and I just defended my PhD in mathematics at MIT. In the fall, I will begin a postdoc research position at Dalhousie University. In 2027, I will move to the Perimeter Institute for Theoretical Physics.

Before MIT, I completed my undergraduate degree at Harvard and my master's degree through Part III at the University of Cambridge. In high school, I participated in the Hampshire College Summer Studies in Mathematics.

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

My current email can be found here.

Krulewski_PhD_Thesis_final.pdf

Papers

• 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

• Homotopical Methods for Free and Interacting Fermionic SPTs - Harvard Center for Mathematical Sciences and Applications - 3.31.25
  • Video
• Twisted Atiyah-Bott-Shapiro Maps - Homotopy Theory Special Session at the Joint Math Meetings 2025 in Seattle - 1.11.25
  • Slides
• Free-to-Interacting Maps and the Bott Spiral - Beijing Institute of Mathematical Sciences and Applications TQFT and Higher Symmetries Seminar - 12.9.24
• Dagger Categories and Higher Spin Statistics - University of Kentucky Topology Seminar - 12.5.24
• Free-to-Interacting Maps and the Bott Spiral - Perimeter Institute for Theoretical Physics - 10.15.24
• Free-to-Interacting Maps and the Bott Spiral - Ohio State University Online Quantum Symmetry Seminar - 10.8.24
• Free-to-Interacting Maps and the Bott Spiral - Anomalology Online Physics Seminar - 9.17.24
  • Video
• Equivariant Witt Complexes - Special Session on Equivariant Algebra at Joint Math Meetings 2024 - 1.3.24
• A Long Exact Sequence in Symmetry Breaking - UCLA Condensed Matter Journal Club - 12.6.23
  • Slides
• A Long Exact Sequence in Symmetry Breaking with Yu Leon Liu - Harvard CMSA Quantum Matter Seminar - 11.7.23
  • Video