Jeffrey L. Jauregui

Harvey Mudd College Mathematics 2005

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Thesis Proposal: Volume Minimizing Cycles in G2-Manifolds
Thesis Advisor: Prof. Weiqing Gu
Second Reader: Prof. Jon Jacobsen
E-Mail: jjauregui@hmc.edu
Final Talk: HMC Presentation Days 2005 Slides
Senior Thesis: Solving for Volume-Minimizing Cycles in G2 Manifolds

Abstract

M-theory, a generalization of string theory, motivates the search for examples of volume-minimizing cycles in Riemannian manifolds of G2-holonomy. Methods of calibrated geometry lead to a system of four coupled nonlinear partial differential equations whose solutions correspond to associative submanifolds of R7, which are 3-dimensional and minimize volume in their real homology classes. Several approaches to finding new solutions are investigated, the most interesting of which exploits the quaternionic structure of the PDE system.

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