Connectedness in dynamics (Laurent Bartholdi (Université de Saarbruecken)

11.10.2022 09:15

Consider the space of complex rational maps of given degree $d$; this space is clearly connected. What about its dynamically-defined subloci? For example, the space of degree-$2$ rational maps one of whose critical points is periodic of period $n$ was conjectured by Milnor to be connected, and this was proven for all $n\le 19$. I will discuss such results, and a topological analogue for which I can prove connectedness for all periods. I will explain why such statements are essentially group-theoretical problems, and how group theory is useful to solve them.

Lieu

Bâtiment: Conseil Général 7-9

Room 1-05, Tuesday 11.10.2022, Attn. unusual time, Séminaire "Groupes et géométrie"

entrée libre