Mike ZIeve (IAS)
The intersection of subfields of K(x)
Given subfields K(f(x)) and K(g(x)) of the field K(x) of rational
functions over a field K, what is their intersection? Is it bigger than K?
I will discuss this problem and some applications and related topics,
including reducibility of polynomials of the form f(x)-g(y), intersections
of orbits of points under complex polynomials, and Diophantine equations
with infinitely many solutions.