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Research interests
My main research interest is Riemannian manifolds with special holonomy. A manifold of dimension n is a space that can be described locally using n coordinates, but which need not be flat. For instance, the usual notion of a surface corresponds to a 2-dimensional manifold. For a manifold to have special holonomy means that it carries some special "parallel" structure.
I am particularly interested in the two exceptional cases in the classification of Riemannian holonomy: 7-manifolds with holonomy G_2 and 8-manifolds with holonomy Spin(7). I study these objects using a combination of tools from differential and algebraic geometry, geometric measure theory and differential topology.
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Projects
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Student Bursary for Joseph Martin - The Matching Problem for Twisted Connected Sum G2-Manifolds
3/07/17 → 8/09/17
Project: UK charity
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Complete noncompact G2-manifolds from asymptotically conical Calabi-Yau 3-folds
Foscolo, L., Haskins, M. & Nordstrom, J., 15 Oct 2021, In: Duke Mathematical Journal. 170, 15, p. 3323-3416 94 p.Research output: Contribution to journal › Article › peer-review
Open AccessFile12 Downloads (Pure) -
Construction of G_2-instantons via twisted connected sums
Menet, G., Nordstrom, J. & Sá Earp, H., 13 May 2021, In: Mathematical Research Letters. 28, 2, p. 471-509 39 p.Research output: Contribution to journal › Article › peer-review
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Exotic G2-manifolds
Crowley, D. & Nordström, J., 1 Oct 2021, In: Mathematische Annalen. 381, 1-2, p. 29–74 46 p.Research output: Contribution to journal › Article › peer-review
Open Access -
Infinitely many new families of complete cohomogeneity one G2-manifolds: G2analogues of the Taub-NUT and Eguchi-Hanson spaces
Foscolo, L., Haskins, M. & Nordström, J., 31 Dec 2021, In: Journal of the European Mathematical Society. 23, 7, p. 2153-2220 68 p.Research output: Contribution to journal › Article › peer-review
Open Access -
An analytic invariant of G2 manifolds
Crowley, D., Goette, S. & Nordström, J., 3 Nov 2020, (arXiv).Research output: Working paper / Preprint › Working paper