Jamie Juul : Backward Orbits of Critical Points

Posted by Nicole Looper , part of the Unlikely Intersections Seminar.

At

Feb. 16, 2023, 2 p.m.

In

636 SEO

Abstract

We study the Galois groups of the extensions $K((f'\circ f^n)^{-1}(0))/K$ where $K$ is a number field for polynomials $f(x)\in K[x]$. We use the results to study the proportion of primes for which $f$ has a $p$-adic attracting periodic point for a "typical" $f$ and apply the statement to the split case of the Dynamical Mordell-Lang Conjecture.