Tom Tucker (Rochester)
Dynamical Manin-Mumford, dynamical Mordell-Lang
The Manin-Mumford and Mordell-Lang conjectures (now theorems of
Raynaud and Faltings, respectively) are among the cornerstones of
modern arithmetic geometry. We will introduce natural dynamical
analogs of each and present a variety of theorems as well some
counterexamples. Roughly speaking, there is a natural one-parameter
analog of Mordell-Lang that is true under some reasonable hypotheses,
while the obvious dynamical analog of Manin-Mumford fails under the
same hypotheses. We will explain why this is perhaps not surprising.