# Mathematical Sciences Research Institute

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# Seminar

Odoni's Conjecture on Iterated Polynomials and Algebraic Extensions of $\mathbb Q$ August 01, 2022 (02:15 PM PDT - 03:00 PM PDT)
Parent Program: Definability, Decidability, and Computability in Number Theory, part 2 MSRI: Simons Auditorium, Online/Virtual
Speaker(s) Philip Dittmann (TU Dresden)
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Video

#### Odoni's Conjecture On Iterated Polynomials And Algebraic Extensions Of $\Mathbb Q$

Abstract/Media

In the field (now) known as Arithmetic Dynamics, Odoni in 1985 conjectured a sweeping statement about Galois groups of iterated polynomials over arbitrary Hilbertian fields, which was decisively disproved by fellow MSRI postdoc Borys Kadets and myself during the first part of the DDC programme. I will give a gentle introduction to the problem, and indicate how counterexamples are ubiquitous even among algebraic extensions of the rational numbers. I will particularly highlight some aspects of the construction of counterexamples of interest to the Hilbert 10 community.

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