Mark Haskins
Professor of Mathematics

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 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

Contact Information

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