To earn an A, a student may turn in homework exercises (say about 20 counting parts of problems as separate problems... exercise 20 counts as more than one for example), make a presentation, or turn in a short paper (project) on some topic related to the course.

 For samples and references (and maybe even ideas)  for such projects, see Professor Freed's  Atiyah-Singer course or Professor Hausel's  Riemannian Geometry course.  Some of the topics in those papers will be covered as course material.  However, there is always more to say than will be covered in the lectures, so it is fine to choose one of the topics on the syllabus. You are encouraged to choose one of the later topics as, if we do get to those topics, we will discuss them only briefly. You may also get some ideas from looking at the notes for Steve Bradlow's more advanced course at the University of Illinois. You can also discuss it with Professor Uhlenbeck when you make the required visit to her office during the term.

Remember when you decide on your topic that this course on Vector Bundles is intended to be preparation for courses at the level of the three courses listed above.

Students may work together and turn in joint projects.

             Suggestions for topics

• Any topic in physics which is related to gauge theory
• spinors and Dirac operators (in Euclidean space or on a manifold)
• Kaluza-Klein theory
  
• The space of SU(2) instantons  on R⁴with k = 1
• The Hopf fibration
• Octonians; describing S⁷ as a fibration
• Mobius transformations
  
• The conformal group of Sⁿ
• Flat bundles on a Riemann surface
• Hodge theory (on manifolds)
  
• Huygen's Principle (for solutions of the wave equation in 3-d)
  
• Nahm's equations
• Chern classes
  
• Chern-Simons Theory
• Seiberg-Witten equations
• Examples of special Lie groups  (for example G₂ or E₈.)
  
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