Michael Zieve The lattice of subfields of K(x) Monday, March 3, 4:00-5:00pm Abstract: I will present various results related to the lattice of fields between K and K(x), where K is a field. ?Topics include: computing the intersection of two subfields of K(x); reducibility of `variables-separated' polynomials f(x)-g(y); and a proof that complex polynomials f and g of degree at least two have orbits with infinite intersection if and only f and g have a common iterate.