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Mark Haskins

Professor of Mathematics
Mathematics
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

Overview


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.

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.

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.



Current Appointments & Affiliations


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

Education, Training & Certifications


University of Texas, Austin · 2000 Ph.D.