Naruki Masuda's Home Page

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

I am a postdoc at Hamburg since October 2024. I graduated from Johns Hopkins in August 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 $(\infty, \infty)$-categorical generalization of spectra (as in homotopy theory). We introduce the (Gray-type) tensor product of categorical spectra and study the notion of stability from the viewpoint of absolute (co)limits. As an application, we derive the cobordism hypothesis with singularities from the plain version of the cobordism hypothesis. While this is the version I submitted for the thesis defense, I hope to improve it slightly before uploading to it arXiv, etc.

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]
• 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

• Here are the recordings for Ambidexterity learning seminar fall 2023 (JHU account required).
• I co-organize JHU topology seminar since fall 2022.
• I organized prismatic cohomology seminar spring 2023 with David Gepner and Milton Lin.

Notes