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Research Interests:
Research Interests:
My research interests concern triangulated categories and higher categories such as: dg-categories, A∞-categories and stable ∞-categories. Some of my work is inspired by problems related to Homological Mirror Symmetry. I am also interested in some aspect of noncommutative motives and Grothendieck duality for schemes and algebraic stacks. I have recently become interested in lifting exact functors between derived categories and in Fourier-Mukai functors.
Papers:
Papers:
X. Chen, M. Ornaghi, A remark on fibrancy of (A∞cat, W), 2025, To appear in Homotopy, Homology and Applications.
M. Ornaghi, Tensor product of A∞-categories, J. Pure Appl. Algebra, 229, Issue 7, 2025, 36 pages, DOI:10.106/j.jpaa.2025.107987.
M. Ornaghi, The Homotopy Theory of A∞-categories, Int. Math. Res. Not., 2025, Issue 11, 2025, 59 pages, DOI:10.1093/imrn/rnaf127.
A. Canonaco, M. Ornaghi, and P. Stellari, Localization of the category of A∞-categories and Internal Homs, Doc. Math. 24, 2019, pp. 2463-2492, DOI: 10.25537/dm.2019v24.2463-2492.
M. Ornaghi, L. Pertusi, Voevodsky's conjecture for cubic fourfolds and Gushel-Mukai fourfolds via noncommutative K3 surfaces, J. Noncommut. Geom. 13, Issue 2, 2019, pp. 499–515, DOI:10.4171/JNCG/328.
Preprints:
Preprints:
A. Canonaco, M. Ornaghi, and P. Stellari, Localization of the category of A∞-categories and Internal Homs over a ring, arXiv:2404.06610, 2024, (40 pages). Submitted.
M. Ornaghi, A comparison between pretriangulated A∞-categories and ∞-categories stable, pdf arXiv:1609.00566, (22 pages). Submitted.
M. Ornaghi, A model structure on the category of A∞-categories with strict morphisms, arXiv:2506.22847, 2025, (9 pages). Submitted.
F. Amodeo, R. Moschetti, M. Ornaghi, Equivalences of derived categories of equivariant sheaves, arXiv:1810.13290, (19 pages).
M. Ornaghi, S. Singh and A. Yekutieli, Rigid Dualizing Complexes and their Functorial Properties, arXiv:2402.07150, 2024, (119 pages).
PhD Thesis:
PhD Thesis:
Comparison results about dg-categories, A∞-categories, stable ∞-categories and noncommutative motives
You can find my thesis here.
You can find the slides of my defence here.
During my PhD I wrote a blog on my mathematical interests.
Master Thesis:
Master Thesis:
Smashing subcategory and the Telescope Conjecture
You can find my thesis here.
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