Jeffrey L. Jauregui
Harvey Mudd College Mathematics 2005
| 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.