[Dottorcomp] Fwd: I: Avviso di seminario Matematico e Fisico di Milano

[Stefano Lisini]

Segnalo il seguente seminario organizzato dal Seminario Matematico e
Fisico di Milano. Non mi hanno comunicato il link zoom, ma dovrebbe
essere disponibile prima del seminario sulla pagina web
https://www.mate.polimi.it/smf/index.php?settore=home&id_link=10

Cordiali saluti,
Stefano Lisini.


Si avvisa che in data 21/7/2021, alle ore 18:00, On line, nell'ambito
delle iniziative del Seminario Matematico e Fisico di Milano, si
svolgerà il seguente seminario:

Holomorphic motions, analytic capacity and conformal welding
Malik Younsi, University of Hawaii
The notion of a holomorphic motion was introduced by Mané, Sad and
Sullivan in the 1980\'s, motivated by the observation that Julia sets
of rational maps often move holomorphically with holomorphic
variations of the parameters. In the years that followed, the study of
the behavior of various set-functions under holomorphic motions became
an area of significant interest. For instance, holomorphic motions
played a central role in the work of Astala on distortion of Hausdorff
dimension and area under quasiconformal mappings.

In this talk, I will first review the basic notions and results
related to analytic capacity and holomorphic motions, including the
extended lambda lemma. I will then present some recent results on the
behavior of analytic capacity under holomorphic motions. The proofs
involve different notions such as conformal welding, quadratic Julia
sets and harmonic measure. This is joint work with Tom Ransford and
Wen-Hui Ai.