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Mark Haskins, Professor

Mark Haskins

My research concerns problems at the intersection between Differential Geometry and Partial Differential Equations, particularly special geometric structures that arise in the context of holonomy in Riemannian geometry. Currently I am particularly interested in special types of 7-dimensional spaces called G2-holonomy manifolds, or G2-manifolds for short. These spaces also arise naturally in modern theoretical physics in the 11-dimensional theory known as M theory. To get from 11 dimensions down to 4 dimensions it is necessary to 'compactify' on a 7-dimensional space and to preserve the maximal degree of (super)symmetry this 7-dimensional space should have G2-holonomy. In fact realistic 4-dimensional physics appears to demand singular G2-holonomy spaces and trying to construct compact singular G2-holonomy spaces is one of my current research projects.

Manifolds with special holonomy also come equipped with special submanifolds, called calibrated submanifolds, and special connections on auxiliary vector bundles, called generalised instantons. I am particuarly interested in associative and coassociative submanifolds in G2-holonomy spaces and special Lagrangian submanifolds in Calabi-Yau spaces. In the past I have also studied singular special Lagrangian n-folds.

I am currently the Deputy Director of the Simons Collaboration Special Holonomy in Geometry, Analysis, and Physics. My colleague here at Duke, Robert Bryant, is the Collaboration Director.

Contact Info:
Office Location:  187 Physics Building, 120 Science Drive, West Campus, Durham, NC 27708-0320
Office Phone:  (919) 660-2800
Email Address: send me a message
Web Pages:  https://www.lms.ac.uk/publications/jlms
https://sites.duke.edu/scshgap/our-team/

Education:

Ph.D.University of Texas at Austin2000
Keywords:

Differential equations, Elliptic • Einstein manifolds • Geometric analysis • Geometric measure theory • Geometry, Riemannian • Holonomy groups • Partial differential equations on manifolds; differential operators

Recent Publications   (More Publications)

  1. Foscolo, L; Haskins, M, New G2-holonomy cones and exotic nearly Kahler structures on S6 and S3 x S3, Annals of Mathematics, vol. 185 no. 1 (January, 2017), pp. 59-130 [doi]  [abs]
  2. Corti, A; Haskins, M; Nordström, J; Pacini, T, G2-Manifolds and associative submanifolds via semi-fano 3-folds, Duke Mathematical Journal, vol. 164 no. 10 (January, 2015), pp. 1971-2092 [doi]  [abs]
  3. Mark, H; Hein, HJ; Johannes, N, Asymptotically cylindrical Calabi-Yau manifolds, Journal of Differential Geometry, vol. 101 no. 2 (January, 2015), pp. 213-265  [abs]
  4. Corti, A; Haskins, M; Nordström, J; Pacini, T, Asymptotically cylindrical Calabi-Yau 3-folds from weak Fano 3-folds, Geometry & Topology, vol. 17 no. 4 (July, 2013), pp. 1955-2059 [doi]  [abs]
  5. Haskins, M; Kapouleas, N, The geometry of SO(p) × SO(q)-invariant special Lagrangian cones, Communications in Analysis and Geometry, vol. 21 no. 1 (April, 2013), pp. 171-205  [abs]
Recent Grant Support

  • Special Holonomy in Geometry, Analysis, and Physics, Simons Foundation, 2016/07-2020/06.      

 

dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821

Mathematics Department
Duke University, Box 90320
Durham, NC 27708-0320