Polynomial decomposition
Mike Zieve

We consider the operation of composition on univariate polynomials over a field K. If K has characteristic zero, Ritt (1921) showed precisely the extent of non-uniqueness of the decomposition of a polynomial into indecomposable polynomials. After reviewing Ritt's results, I will discuss new results and examples in the much more complicated situation of positive characteristic. I will also discuss the related question of when two subfields of a function field intersect in more than just constants.