arXiv subjects

Naruki Masuda

Publications and source records attributed to Naruki Masuda.

3 recordsLinked to original sources

arXiv2026

The Algebra of Categorical Spectra

Categorical spectra are spectrum objects in pointed $(\infty,\infty)$-categories: sequences $(X_n)$ equipped with equivalences $X_n\simeq \Omega X_{n+1}$. This thesis develops foundations for categorical spectra and constructs their tensor product, the stabilized analogue of the lax Gray tensor product of $(\infty,\infty)$-categories. We use this tensor product to study stability phenomena, expressed as the coincidence of certain finite weighted colimits and limits. As an application, we give a precise categorical derivation of the cobordism hypothesis with singularities from the ordinary cobordism hypothesis, making rigorous a sketch of Lurie.

math.AT↗

arXiv2021

Global critical chart for local Calabi-Yau threefolds

In this paper, we investigate Keller's deformed Calabi--Yau completion of the derived category of coherent sheaves on a smooth variety. In particular, for an $n$-dimensional smooth variety $Y$, we describe the derived category of the total space of an $\omega_Y$-torsor as a certain deformed $(n+1)$-Calabi--Yau completion of the derived category of $Y$. As an application, we investigate the geometry of the derived moduli stack of compactly supported coherent sheaves on a local curve, i.e., a Calabi--Yau threefold of the form $\mathrm{Tot}_C(N)$, where $C$ is a smooth projective curve and $N$ is a rank two vector bundle on $C$. We show that the derived moduli stack is equivalent to the derived critical locus of a function on a certain smooth moduli space. This result will be used by the first author and Naoki Koseki in their joint work on Higgs bundles and Gopakumar--Vafa invariants.

math.AG↗

arXiv2019

The diagonal of the associahedra

This paper introduces a new method to solve the problem of the approximation of the diagonal for face-coherent families of polytopes. We recover the classical cases of the simplices and the cubes and we solve it for the associahedra, also known as Stasheff polytopes. We show that it satisfies an easy-to-state cellular formula. For the first time, we endow a family of realizations of the associahedra (the Loday realizations) with a topological and cellular operad structure; it is shown to be compatible with the diagonal maps.

math.AT↗