mentor: Christopher Woodward
The Yang-Mills equations are important to theories of particle physics
and are mathematically interesting as well. The vortex equations are a
generalization of the Yang Mills equations, and we are considering whether
a solution to these equations can be gauge transformed into a smooth
- 24 Jul: Continued reading about elliptic regularity.
- 17 Jul: REU presentation
- 10 Jul: Started reading about elliptic regularity.
- 03 Jul: Worked on understanding the paper.
- 25 Jun: This past week I have read about connections, curvature,
almost complex structure on manifolds, Kaehler manifolds, and moment
maps. Next week I will work on understanding the content of the paper
A Direct Existence Proof for the Vortex Equations Over a Compact
Riemann Surface (see below).
List of References
- Lee, John M. Introduction to Smooth
Manifolds. New York: Springer, 2006.
- Broecker, Theodor, and Tammo tom Dieck. Representations of Compact
Lie Groups. New York: Springer-Verlag, 1985.
- Kobayashi, Shoshichi, and Katsumi Nomizu. Foundations of
Differential Geometry (vol. I). New York: Interscience, 1963.
- Cannas da Silva, Ana. Lectures on Symplectic
Geometry. Springer-Verlag, 2001.
- Garcia-Prada, Oscar. "A Direct Existence Proof for the Vortex
Equations Over a Compact Riemann Surface." Bull. London
Math. Soc. 26 (1994): 88-96.