Matthew Holden

Harvey Mudd College Mathematics 2004

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Thesis Proposal: mholden-2004-prop.pdf
Thesis Advisor: Prof. Weiqing Gu
Second Reader: Prof. Sandy Grabiner
E-Mail: matthew.holden@pomona.edu

Volume Minimizing Cycles in G2-Manifolds

Manifolds with special holonomy group G2 (the automorphism group of the octonians) have recently received much attention in connection with superstring theory in physics. More specifically, some promising attempts to unify the various flavors of string theory under a single unified ''M-theory'' suggest that our universe may have the structure of such a manifold.

I will use the theory of calibrated geometry to identify and study associative and co-associative subvarieties of a specific G2-manifold. Such subvarieties are calibrated by certain alternating forms, and they are important because they are volume minimizing in their homology classes. More specifically, I will search for volume minimizing cycles in R6 × S1, with an eventual aim of classifying these submanifolds.