After reviewing ordinary finite-dimensional Morse theory, I will explain how Morse generalized Morse theory to loop spaces, and how Floer generalized it to gauge theory on a three-manifold. Then I will describe an analog of Floer cohomology with the gauge group taken to be a complex Lie group (rather than a compact group as assumed by Floer), and how this is expected to be related to the Jones polynomial of knots and Khovanov homology.
• Geometry and Holomony
• Supersymmetry, Spinors, and Calabi-Yau
• Flux and Backreaction
• Energetics of Heterotic Flux Compactification
• Strominger System and Heterotic Flux as a Torsion
• A Supersymmetric Solution to Heterotic Flux Compactification
• Global Issues: Index Counting, Smoothness, etc