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Graduate Student Number Theory Learning Seminar

Automorphism groups of dynamical systems over finite fields

Max Weinreich (Brown University)

Date & time: Wednesday, 29 April 2020 at 9:20AM - 10:20AM


What does it mean for a dynamical system to have symmetry? In this talk, we will define automorphism groups of dynamical systems and look at the particular case of self-maps of the projective line over any field. In complex dynamics, the possible automorphism groups come from platonic solids: evidence of classical geometry. But what about when the base field is a finite field F_p? Just like with other algebraic objects – say, curves or abelian varieties – the possible automorphism groups are much more diverse in characteristic p. First we will look at the set of maps with automorphisms in the moduli space of maps of degree 2. Then we will talk about how maps with prescribed automorphism group are constructed in complex dynamics, and how we modified these methods so that they could still work over finite fields. Joint work with Cai, Hutz, and Mayer.

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