SIMBa: Unlikely Intersections in Dynamics

24/02/2022 by blocmat Deixa un comentari

El proper dimecres, 2 de març, se celebrarà una nova xerrada del Seminari Informal de Matemàtiques de Barcelona (SIMBa).

Speaker: Andriana Karuk
Universitat:

Data: Wednesday, March 2nd, 2022.
Hora: ~~12:00, coffee break; 12:20, talk~~. Actualització: 12:00, virtual coffee break ; 12:20, talk.
Lloc: Zoom, UB (aula B1).
Idioma: English.

Títol: Unlikely Intersections in Dynamics
Resum: Arithmetic dynamics is an encounter of number theory and dynamical systems. In arithmetic dynamics, one focuses on studying properties of self-maps with a flavour of number theory. In particular, the study of unlikely intersections in arithmetic geometry leads to dynamical problems of an arithmetic nature. The guiding principle is that families of objects should not intersect unless there is a geometric reason forcing the converse. Our object of study is the set of parameters $c \in \mathbb{C}$ such that both $a$ and $b$ are preperiodic for $f_{c}(z)=z^{d}+c$ . We will see that for any fixed $a, b \in \mathbb{Z}$ and any integer $d \geqslant 2$ , the set of $c \in \mathbb{C}$ for which both $a$ and $b$ are preperiodic for $z^{d}+c$ is infinite if and only if $a^{d}=b^{d}$ . The proof combines complex-analytic and arithmetic tools to prove this statement, which we will have a glimpse of.

Si voleu estar al cas de les xerrades previstes, podeu consultar el calendari. Si voleu proposar una xerrada, ompliu el formulari. Si voleu contactar amb els responsables podeu escriure un missatge a seminari(dot)simba(at)ub(dot)edu.