nikolkuh

• Kuhn, Nikolas Thomas Urs (2024). Spin structures on perfect complexes. arXiv. doi: 10.48550/ARXIV.2410.20623. Full text in Research Archive
• Asgeirsson, Dagur; Brasca, Riccardo; Kuhn, Nikolas Thomas Urs; Majno, Filippo Alberto Edoardo Nuccio Mortarino & Topaz, Adam (2024). CATEGORICAL FOUNDATIONS of FORMALIZED CONDENSED MATHEMATICS. Journal of Symbolic Logic (JSL). ISSN 0022-4812. doi: 10.1017/jsl.2024.69. Full text in Research Archive Show summary

  Condensed mathematics, developed by Clausen and Scholze over the last few years, proposes a generalization of topology with better categorical properties. It replaces the concept of a topological space by that of a condensed set, which can be defined as a sheaf for the coherent topology on a certain category of compact Hausdorff spaces. In this case, the sheaf condition has a fairly simple explicit description, which arises from studying the relationship between the coherent, regular, and extensive topologies. In this paper, we establish this relationship under minimal assumptions on the category, going beyond the case of compact Hausdorff spaces. Along the way, we also provide a characterization of sheaves and covering sieves for these categories. All results in this paper have been fully formalized in the Lean proof assistant.

• Kuhn, Nikolas Thomas Urs; Asgeirsson, Dagur; Topaz, Adam; Brasca, Riccardo & Nuccio, Filippo (2024). Categorical Foundations of Formalized Condensed Mathematics. arXiv.org. ISSN 2331-8422. doi: 10.48550/arXiv.2407.12840. Full text in Research Archive
• Kuhn, Nikolas Thomas Urs (2024). The Atiyah class on algebraic stacks. Forum of Mathematics, Sigma. 12. doi: 10.1017/fms.2024.109. Full text in Research Archive Show summary

  We generalize Illusie’s definition of the Atiyah class to complexes with quasi-coherent cohomology on arbitrary algebraic stacks. We show that this gives a global obstruction theory for moduli stacks of complexes in algebraic geometry without derived methods. We give a similar generalization of the reduced Atiyah class, and we show various useful properties for working with Atiyah classes, such as compatibilities between the reduced and ordinary Atiyah class, and compatibility with tensor products and determinants.

• Thimm, Felix; Liu, Henry & Kuhn, Nikolas Thomas Urs (2023). The 3-fold K-theoretic DT/PT vertex correspondence holds. arXiv.org. ISSN 2331-8422. doi: 10.48550/arXiv.2311.15697. Full text in Research Archive
• Kuhn, Nikolas Thomas Urs (2023). Degenerations of Sheaves on Fibered Surfaces. arXiv.org. ISSN 2331-8422. doi: 10.48550/arXiv.2305.19984. Full text in Research Archive

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• Kuhn, Nikolas Thomas Urs (2024). Spin structures on perfect complexes. Full text in Research Archive
• Kuhn, Nikolas Thomas Urs (2024). Wall-crossing for Vafa-Witten invariants. Full text in Research Archive
• Kuhn, Nikolas Thomas Urs (2023). Degeneration of Sheaves on Fibered surfaces. Full text in Research Archive
• Kuhn, Nikolas Thomas Urs (2023). Degenerations of Sheaves on Fibered Surfaces. Full text in Research Archive
• Kuhn, Nikolas Thomas Urs (2023). The Atiyah class on algebraic stacks. arXiv.org. ISSN 2331-8422. doi: 10.48550/arXiv.2306.13934. Full text in Research Archive
• Kuhn, Nikolas Thomas Urs (2022). The Blowup Formula for the Instanton Part of Vafa-Witten Invariants on Projective Surfaces. Full text in Research Archive

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