Time: Friday, July 6 from 2:00 – 4:00 pm
Location: Keller 401
Draft of dissertation
Abstract: \
We provide some general tools that can be used for polynomials in any degree to show $G_\infty = \text{Aut}(T_\infty)$. We introduce the idea of Newton irreducibility to help push us closer to a proof to Odoni’s conjecture for monic integer polynomials when $d=4$. We also show that current techniques used in the literature will not work in proving Odoni’s conjecture for monic quartic polynomials. Finally, we look at how certain behaviors of the critical points of a polynomial $f(x) \in \mathbb{Q}[x]$ force it to not have full Galois image.