This is the website for the INDAM Meeting "New Trends in Holomorphic Dynamical Systems", that will take place between August 29th and September 2nd 2022, at the Palazzone di Cortona.

Dynamical systems occupy a prominent role in contemporary mathematics. Among them, holomorphic dynamical systems take a notable position.
While research in holomorphic dynamics has traditionally been devoted to the one-dimensional case, in the last decades more and more effort has been put in building a theory valid in any dimension. This has dramatically increased the connections with other fields, among them ergodic theory, (pluri)potential theory, algebraic geometry, arithmetic geometry, complex geometry and analysis. In order to foster the exchanges between researchers working in one and in several complex variables, a large INDAM conference was organized in Cortona in September 2012. A number of collaborations started on that occasion, and many young researchers identified at that point contributed to the advance of the domain and are are now taking leading roles in the field.

Since 2012, spectacular progress was made in the area. A number of major open problems was solved, using a combination of local and global techniques; moreover, analogues of theories specific of the one-dimensional case have been developed (or are under active development) in higher dimensions. This has led to an even larger number of promising research directions.

This 2022 conference in holomorphic dynamics at Cortona will allow us to focus on the interplay between local and global techniques. More specifically, here is a brief (non exhaustive) list of the main topics covered in the conference.

• Local dynamics and applications.

• Bifurcation theory; parabolic and semi-parabolic implosion.

• Fatou components: global geometry; wandering domains.

• Iteration of transcendental maps.

• Denjoy-Wolff type results.

• Arithmetic dynamics.

List of speakers:

Matthieu Astorg (Orléans)

Anna Miriam Benini (Parma)

Eric Bedford (Stony Brook)

François Berteloot (Toulouse)

Gautam Bharali (Bangalore)

Sebastien Biebler (Paris)

Filippo Bracci (Roma)

Xavier Buff (Toulouse)

Davoud Cheraghi (London)

Núria Fagella (Barcelona)

Matteo Fiacchi (Roma)

Aleksandra Huczek (Krakov)

Valentin Huguin (Bremen)

Han Peters (Amsterdam)

Sergei Yakovenko (Rehovot)

Anna Zdunik (Warsaw)

Andrew Zimmer (Wisconsin)

(*=to be confirmed)

Scientific committee:

Marco Abate, Leandro Arosio, Fabrizio Bianchi, Jasmin Raissy, Matteo Ruggiero.

Organizing committee:

Leandro Arosio, Fabrizio Bianchi, Jasmin Raissy, Matteo Ruggiero.