Naruki Masuda's Home Page

Contact: nmas!uda!!dot!ma!!th!at!!gm!ail!!!do!tc!om (remove exclamation marks)

I am a BOAS assistant professor (postdoc) at Northwestern University since September 2025. Before that, I was a postdoc at Hamburg (CRC 1624) 2024-2025 and a graduate student at Johns Hopkins 2018-2024. I am interested in homotopy theory, topology, category theory, and related topics. Here is my CV (last updated: September 2024)

Thesis

• The Algebra of Categorical Spectra: Categorical spectra are an $(\infty,\infty)$-categorical generalization of spectra in homotopy theory. We introduce a Gray-type tensor product of categorical spectra and study stability from the viewpoint of absolute (co)limits. As an application, we derive the cobordism hypothesis with singularities from the ordinary cobordism hypothesis. This is a revision of the original version. Many proofs have been improved, but statements about the state of the field should be read as reflecting the situation as of July 2024.

Publications

• Global critical chart for local Calabi-Yau threefolds [arXiv]: For an $n$-dimensional smooth variety $Y$, we describe the derived category of the total space of a $\omega_Y$-torsor as a certain deformed (n+1)-Calabi--Yau completion of the derived category of $Y$. The result is used by Tasuki Kinjo and Naoki Koseki to prove the cohomological chi-independence conjecture for Gopakumar--Vafa invariants. Joint work with Tasuki Kinjo.
• The Diagonal of the Associahedra: A new geometric/combinatorial way to understand and construct Alexander-Whitney type maps of polytopes applied to associahedra. Joint work with Hugh Thomas, Andy Tonks and Bruno Vallette.

Research Talks with notes

• Stability of categorical spectra and an application to TQFT, Research Seminar on Quantum Topology and Categorification, Nov 1, 2024 [notes]
• The first step towards higher^2 algebra, TGTS Tetrahedral Geometry/Topology Seminar, Elizabethtown College, September 8, 2023. [notes]
• Tensor product of categorical spectra, 高知ホモトピー論談話会 (Kochi homotopy theory workshop), December 28, 2022 [notes]
• The diagonal of the associahedra, UPenn Deformation Theory Seminar, November 1, 2021 [notes]
• The slides for the Oral exam, March 2021. Warning: The ideas here are preliminary and many are misleading or wrong.

Seminars and Workshops

• I co-organized FRG workshop on higher categories and geometry in March 2026 and gave a minicourse.
• I co-organized Research Seminar on Quantum Topology and Categorification (QTCat) 2024-2025.
• Here are the recordings for Ambidexterity learning seminar fall 2023 (JHU account required).
• I co-organized JHU topology seminar 2022-2024.
• I organized prismatic cohomology seminar spring 2023 with David Gepner and Milton Lin.

Miscellaneous

• A lax guide to oplax tensor product convention
• How to write hiragana よ
• 数理科学 2025年9月号 No. 747 多彩な拡がりをもつ《層》の魅力 特集記事 代数トポロジーと層 (expository magazine article on Algebraic Topology and Sheaves)
• Higher Category Theory, March 2025 Some notes for a course I gave in Hamburg.
• notes on past JHU quals algebra problems from when I lead review sessions for first-year graduate students (may contain wrong solutions. large file).