[EstudiantesMatemática]Seminario sistemas dinámicos

[lpineyrua]

Hola,

Este viernes 19/07 a las 14:30 en el Salón de seminarios del IMERL  
(101) tendremos el placer de escuchar a Arcelino Lobato (IMPA).

Título: On the combinatorial-topology of branched covers of the sphere.

Resumen: In the 2010's, Thurston was considering the question of  
understanding holomorphic mappings from the topological point of view.  
At that time, he introduced the balanced planar 4-regular graphs and  
showed that they combinatorially characterize all cell graph  
Γ=f^{−1}(Σ) ⊂ S_2  where f:S_2→S_2 is an generic  
orientation-preserving degree d branched covering, and Σ ⊂ S_2 is an  
oriented Jordan curve passing through the critical values of f (the  
word generic means that the cardinality of the set of critical values  
of f is 2d−2, the largest possible). In this talk we will provide a  
combinatorial presentation for a branched cover of the 2-sphere  
generalizing completely the mentioned Thurston’s theorem. We will see  
that the most natural generalization of the balance condition for  
higher genera does not suffice for the realizability of a cell graph  
as a pullback graph Γ. Then, with one more imposition, we provide our  
mean result. After that, we will introduce and go over some operations  
defined on the (generalized) balanced graphs and mention some further  
results, if time permits.


El seminario se transmite por el siguiente link si alguien manifiesta  
interés hasta el día antes del seminario:
https://salavirtual-udelar.zoom.us/j/83020032334?pwd=djAxdmg2K3NDVEU0V3RZSXkxNW8xUT09

Saludos,
Santiago Martinchich y Luis Pedro Piñeyrúa.