Thomas Gauthier (Université Paris Saclay)

will speak on

Postcritically finite endomorphisms of projective spaces

Time: 3:00PM
Date: Tue 15th October 2024
Location: E0.32 (beside Pi restaurant) [map]

Further information

Abstract: An endomorphism of the projective space P^k of dimension k is postcritically finite if its critical set C(f) is pre-periodic under iteration of the map f, i.e. if there are integers n > m ≥ 0 such that f^n(C(f)) is included in f^m(C(f)). When k ≥ 2, it is conjectured by Ingram, Ramadas and Silverman that such maps are not Zariski dense in the space of all endomorphisms of a given degree d ≥ 2.
In a work in common with Johan Taflin and Gabriel Vigny, we show this conjecture and we further give a uniform bound on the number of pre-periodic points lying in the critical set of a general regular polynomial endomorphism of the affine plane of a given degree.

In this talk I will start with presenting a motivation: the distribution of periodic points of a given endomorphism. Then I will discuss what happens in families of rational maps of the Riemann sphere. If we have time, I will finish with a sketch of the strategy of the proof of the non-Zariski density of such parameters in the space of endomorphisms of P^k, k ≥ 2.

https://ucd-ie.zoom.us/j/66387552574

(This talk is part of the Analysis series.)

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