Shinobu Yokoyama
Independent researcher in mathematics (Algebraic Topology)
Research Interests
My primary research interests are in homotopy theory and its foundational frameworks, including model categories, higher categorical structures, and homotopical notions of stability and coherence. These interests shape both the questions I regard as fundamental and the criteria by which I evaluate definitions and invariants.
My current research concentrates on contexts where such homotopical ideas can be examined through explicit and controllable models. In particular, I study sheaves and cosheaves on cell complexes and related stratified spaces, viewed as concrete settings in which local-to-global phenomena and structural obstructions can be analyzed and made precise.
A recurring aspect of this work is the use of classical algebraic topological machinery—such as spectral sequences, Morse-theoretic techniques, and discrete or stratified Hodge-type methods—to extract and compare invariants in finite or combinatorial situations. I am also interested in directed topological structures, where classical homotopy invariance breaks down and foundational issues re-emerge in a restricted but explicit form.
While my long-term interests lie in foundational aspects of modern homotopy theory, my current work emphasizes settings in which arguments can be completed and phenomena can be studied concretely.
Preprint
- Relative Obstructions and Spectral Diagnostics for Sheaves on Cell Complexes, 2026
– arXiv:2601.19056 (math.AT)
Talks
- “Spectral Identification of Logical Defects: An Inverse Problem on Cellular Sheaves”
– Poster and Talk session at Finland-Japan Workshop in Industrial and Applied Mathematics 2026
– ResearchGate
Background
Before returning to academic research, I worked in industry on mathematically oriented problems. This experience has influenced my interest in finite models, structural robustness, and explicit constructions, which continue to inform my current research.
Information on prior industry experience and applied work is available on a separate practitioner profile.
- B.A. in Music, University of Central Oklahoma, 2007
- M.S. in Mathematics, Kyoto University, 2018
- Independent researcher (current)
Contact
yokoyama.shinobu [dot] 46c [at] kyoto-u [dot] jp
