This will be a practice for (preview of) my candidacy exam. My goal is that this talk will make sense to non experts, and I will happily answer lots of questions.

To complete last week's talk, I will continue to speak on integration by parts, with applications.

We introduce infinity harmonic functions and discuss their regularity in two dimensions. In particular we show they satisfy an "improvement of flatness" property which gives interior regularity.

Given a group G of order n, a prime p (not dividing n) acts as a permutation on the conjugacy classes of G by sending each element g to g^p. Previous work determined the sign of this permutation. In this talk we will determine the conjugacy class (ie cycle type) of this permutation. To do this we decompose the group ring of G into a sum of abelian Galois extensions, and then show the cycle type of our permutation corresponds to the splitting of the prime p in these fields.

I will talk about two important moduli problems and give the outline of a construction for thier moduli spaces. Then I will use them to prove Kontsevich's formula, which is the solution to an old problem from classical enumerative geometry. This is my candidacy exam.

No seminar, it's Thanksgiving break.