Counting rational points and lower bounds for Galois orbits.

Harry Schmidt (Manchester)

Frank Adams 1,

We will discuss a method to obtain lower bounds for the growth of certain Galois orbits. We will show how to use this method to prove polynomial lower bounds for Galois orbit of torsion points of one dimensional group varieties. This can be established using the theory of real Pfaffian differential equations, in particular work of Pila and Jones, Thomas. Time permitting we will also discuss some application to polynomial dynamical systems.

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