We are looking to run a working seminar about the Yang-Mills story. We hope that our seminars is of interest to analysts (working with curvatures and Ricci flows on Riemannian manifolds), the algebraists (working on Lie algebras and Lie groups), and, of course, math physicists. If we manage to understand something about the Clay problem in this direction, that would be great, but it is not strictly necessary. 


The seminar is to run for a year. It involves talks by graduate students, postdocs, and faculty (almost all from the maths department). I'm looking for helpful references. 



References for Yang-Mills Theory
If your goal is to get some understanding of the Clay Problem, you can't really go wrong with first reading the [official problem statement](http://www.claymath.org/sites/default/files/yangmills.pdf) and then reading the papers referred to in the document. 




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On the other hand, if your goal is not the quantum problem but more the classical problem, for the geometers and algebraists a good starting point is of course Donaldson's *Geometry of four-manifolds* which contains a lot of classical results in the direction (and you can use the reference list to find the original papers should you wish). Donaldson's more recent [survey](http://wwwf.imperial.ac.uk/~skdona/YMILLS.PDF) can also be a point of departure. 


Since you mentioned that there are participants interested in curvature and Ricci flows, you can also consider discussing the results related to the Yang-Mills heat flow. The standard references are


* *Johan Råde*, MR 1179335 [**On the Yang-Mills heat equation in two and three dimensions**](http://dx.doi.org/10.1515/crll.1992.431.123), *J. Reine Angew. Math.* **431** (1992), 123--163.
* *Andreas E. Schlatter, Michael Struwe, and A. Shadi Tahvildar-Zadeh*, MR 1600272 [**Global existence of the equivariant Yang-Mills heat flow in four space dimensions**](http://muse.jhu.edu/journals/american_journal_of_mathematics/v120/120.1schlatter.pdf), *Amer. J. Math.* **120** (1998), no. 1, 117--128.


If you also want to discuss the hyperbolic initial value problem, then a good (classical) place to start would be


* Eardley and Moncrief [MathSciNet link](http://www.ams.org/mathscinet-getitem?mr=0649159)
* Choquet-Bruhat and Christodoulou [MathSciNet link](http://www.ams.org/mathscinet-getitem?mr=654209)


There has been *a lot* of development/improvement/extensions since then (see the References link in mathscinet) but they tend to get very technical very fast (into the details of PDE theory for wave equations) and may be less interesting for your stated audience. 


