Amanda Hood


mentor: Christopher Woodward

REU project

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 solution.

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List of References

  1. Lee, John M. Introduction to Smooth Manifolds. New York: Springer, 2006.
  2. Broecker, Theodor, and Tammo tom Dieck. Representations of Compact Lie Groups. New York: Springer-Verlag, 1985.
  3. Kobayashi, Shoshichi, and Katsumi Nomizu. Foundations of Differential Geometry (vol. I). New York: Interscience, 1963.
  4. Cannas da Silva, Ana. Lectures on Symplectic Geometry. Springer-Verlag, 2001.
  5. Garcia-Prada, Oscar. "A Direct Existence Proof for the Vortex Equations Over a Compact Riemann Surface." Bull. London Math. Soc. 26 (1994): 88-96.