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Mark Haskins
Professor of Mathematics

My research concerns problems at the intersection between

Manifolds with special holonomy also come equipped with special submanifolds, called

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 and currently Chair of the Mathematics department.

**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**G**, or G_{2}-holonomy manifolds_{2}-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 G_{2}-holonomy. In fact realistic 4-dimensional physics appears to demand singular G_{2}-holonomy spaces and trying to construct compact singular G_{2}-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 G_{2}-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 and currently Chair of the Mathematics department.

### Current Research Interests

- Riemannian geometry
- Systems of elliptic partial differential equations
- Einstein manifolds, especially Ricci-flat manifolds
- Riemannian metrics with special or exceptional holonomy.
- Minimal submanifolds, particularly calibrated submanifolds
- Calibrated currents and their singularities and regularity, especially special Lagrangian and associative currents
- Singular spaces with special or exceptional holonomy
- Gauge theory on spaces with special and exceptional holonomy
- Riemannian collapse under Ricci-curvature bounds
- Solitons and singularity formation in in geometric flows, especially Bryant's Laplacian flow

### Current Appointments & Affiliations

- Professor of Mathematics, Mathematics, Trinity College of Arts & Sciences 2019

### Contact Information

- 120 Science Drive, 117 Physics Building, Campus Box 90320, Durham, NC 27708-0320
- 187 Physics Building, 120 Science Drive, West Campus, Durham, NC 27708-0320
- mhaskins@math.duke.edu
- Journal of the London Mathematical Society
- Learned Society of Wales
- My lectures in the Simons Collaboration
- Simons Collaboration on Special Holonomy in Geometry, Analysis and Physics

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