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Abelian dynamical Galois groups associated to postcritically finite rational functions

Abelian dynamical Galois groups associated to postcritically finite rational functions

Start: 
Tuesday, February 27, 2024 11:00 am
End: 
Tuesday, February 27, 2024 11:50 am
Location: 
On line
Chifan Leung
OSU Mathematics Department

Andrews and Petsche formulated a conjecture that an arboreal Galois extension is abelian if and only if the polynomial is conjugate to a powering map or a Chebyshev map and the base point is a root of unity in a number field. In this talk, we will discuss if a rational function is postcritically finite, and the base point is not preperiodic, then the arboreal Galois tower is not abelian. This uses two deep theorems, a result by Benedetto-Ingram-Jones-Levy on attracting cycles, as well as an equidistribution result by Baker-Rumely, Favre-Rivera-Letelier and Chambert Loir. This work is jointly by me and my advisor Clayton Petsche.

Contact: 
T Schmidt