Embedded Files
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:
M. Ornaghi, A model structure on the category of A∞-categories with strict morphisms, Appl. Categor. Struct. 34, Issue 29. (2026) DOI:10.1007/s10485-026-09870-2
X. Chen, M. Ornaghi, A remark on fibrancy of (A∞cat, W), (2025) to appear in Homotopy, Homology and Applications.
M. Ornaghi, Some properties of the A∞-nerve, Milan J. Math., 94, 45-70. (2026) DOI:10.1007/s00032-026-00429-3.
M. Ornaghi, Tensor product of A∞-categories, J. Pure Appl. Algebra, 229, Issue 7, 1-36. (2025) DOI:10.106/j.jpaa.2025.107987.
M. Ornaghi, The Homotopy Theory of A∞-categories, Int. Math. Res. Not., 2025, Issue 11, 1-59. (2025) 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, 2463-2492. (2019) 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, 499–515. (2019) DOI:10.4171/JNCG/328.
Preprints:
Preprints:
M. Ornaghi, The (right) homotopy between two A∞-morphisms, arXiv:2610:13803, 2026, (20 pages).
M. Ornaghi, An example of the non-existence of coequalizers in the category of the A∞-categories, arXiv:2610:07017, 2026, (6 pages).
A. Canonaco, M. Ornaghi, New examples of non-Fourier-Mukai exact functors via non-isomorphic octahedra, arXiv:2601.21559, 2026, (15 pages). Submitted.
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.
F. Amodeo, R. Moschetti and 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.
Google Sites
Report abuse