Number Theory (Discrete) Dynamics

I will explain two recent results which lie between
number theory and dynamics. The first result exhibits all
pairs of complex polynomials which have orbits with infinite
intersection. The second result asserts that any polynomial
with rational coefficients induces a function on the rational
numbers which is at most 6-to-1 outside a finite set. I will
also present conjectural generalizations of these two results
which simultaneously generalize the Mordell-Lang conjecture and
Mazur’s theorem on rational torsion on elliptic curves,
respectively.

This talk will be accessible to graduate students.