Mark Haskins

Journal article Duke Mathematical Journal · October 15, 2021 Featured Publication We develop a powerful new analytic method to construct complete noncompact Ricci-flat 7-manifolds, more specifically G2-manifolds, that is, Riemannian 7- manifolds .M;g/ whose holonomy group is the compact exceptional Lie group G2. Our construction gives t ... Full text Open Access Cite

Infinitely many new families of complete cohomogeneity one G2-manifolds: G2analogues of the Taub-NUT and Eguchi-Hanson spaces

Journal article Journal of the European Mathematical Society · January 1, 2021 Featured Publication We construct infinitely many new 1-parameter families of simply connected complete non-compact G2-manifolds with controlled geometry at infinity. The generic member of each family has so-called asymptotically locally conical (ALC) geometry. However, the na ... Full text Cite

New G2-holonomy cones and exotic nearly Kahler structures on S6 and S3 x S3

Journal article Annals of Mathematics · January 1, 2017 Featured Publication There is a rich theory of so-called (strict) nearly Kahler manifolds, almost-Hermitian manifolds generalising the famous almost complex structure on the 6-sphere induced by octonionic multiplication. Nearly Kahler 6-manifolds play a distinguished role both ... Full text Open Access Cite

G2-Manifolds and associative submanifolds via semi-fano 3-folds

Journal article Duke Mathematical Journal · January 1, 2015 Featured Publication We construct many new topological types of compact G2-manifolds, that is, Riemannian 7-manifolds with holonomy group G2. To achieve this we extend the twisted connected sum construction first developed by Kovalev and apply it to the large class ... Full text Cite

Special Lagrangian cones with higher genus links

Journal article Inventiones Mathematicae · February 1, 2007 Featured Publication For every odd natural number g=2d+1 we prove the existence of a countably infinite family of special Lagrangian cones in ℂ3 over a closed Riemann surface of genus g, using a geometric PDE gluing method. © Springer-Verlag 2007. ... Full text Cite

The geometric complexity of special Lagrangian T2-cones

Journal article Inventiones Mathematicae · July 29, 2004 Featured Publication We prove a number of results on the geometric complexity of special Lagrangian (SLG) T2-cones in ℂ3. Every SLG T 3-cone has a fundamental integer invariant, its spectral curve genus. We prove that the spectral curve genus o ... Full text Cite