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.