Simone Diverio, Sapienza. Sviluppi recenti sulla congettura di Lang: quozienti di domini limitati

Martedì 17 maggio ore 16 aula D'Antoni

Abstract:

La congettura di Lang (1986) caratterizza le varietà complesse proiettive (o, più generalmente, Kähler compatte) iperboliche nel senso di Kobayashi come quelle di tipo generale assieme a tutte le loro sottovarietà.

Lungi dall’essere dimostrata al momento, la congettura è però nota in una serie di casi paradigmatici ancorché particolari.

Ci concentreremo in particolare su una direzione della congettura, spiegando come sia possibile verificare ad esempio che un quoziente libero e compatto di un dominio limitato dello spazio affine complesso abbia tutte sottovarietà di tipo generale (lavoro in collaborazione con S. Boucksom).

Tempo permettendo, descriveremo alcune variazioni sul tema, considerando tipi di quozienti più generali: non più necessariamente lisci, né compatti (lavoro in collaborazione con B. Cadorel e H. Guenancia).

Franc Forstnerič, Ljubljana. Oka domains in Euclidean spaces

Giovedì 5 maggio ore 17 aula D'Antoni

Abstract:

We find surprisingly small Oka domains in complex Euclidean spaces of dimension n>1 at the very limit of what is possible. Under mild geometric assumptions on a closed unbounded convex set E in C^n we show that the complement of E is an Oka domain. This holds in particular if E does not contain any affine real line. Hence, there are Oka domains which are only slightly bigger than a halfspace, the latter being neither Oka nor hyperbolic. (Joint work with Erlend F. Wold.)

Anders Karlsson, Genève. Stars in the boundary at infinity of metric spaces

Martedì 15 Marzo ore 16, Aula D'Antoni

Abstract:

We are interested in non-compact complete metric spaces, for example coming from invariant distances on domains in complex vector spaces. In the boundary of compactifications of the spaces, one can define certain invariant subsets, called stars. Intuitively, the purpose of these sets is, on the one hand, to extend features of Gromov hyperbolicity to any metric space to the extent it is possible. Such features include visibility, north-south contractive dynamics of isometries and its consequences, as well as a Wolff-Denjoy theorem for the iterates of non-expansive maps (such as holomorphic maps in the complex analytic context). On the other hand, the stars provide a convenient way of describing the asymptotic geometry of a space. Some open problems and general speculations will be discussed.

Gian Maria Dall'Ara, INdaM-SNS. An uncertainty principle in complex analysis

Martedì 14 Dicembre ore 16, Aula D'Antoni

Abstract:

We present an elementary inequality, which we introduced in a previous work ("Coercivity of weighted Kohn Laplacians...", TAMS 2017), and show how it allows us to import ideas from the theory of Schrödinger operators into several complex variables. The underlying geometry turns out to be connected with the notion of Levi core, recently introduced in a joint paper with Samuele Mongodi ("The core of the Levi distribution", arXiv:2109.04763). The novelties (after the 2017 paper) are all joint work with Samuele Mongodi.

Sarà possibile seguire il seminario su Teams col seguente link:

https://teams.microsoft.com/l/meetup-join/19%3a3132d775a6084c43b6f1d4a2e44c9f78%40thread.tacv2/1639092385346?context=%7b%22Tid%22%3a%2224c5be2a-d764-40c5-9975-82d08ae47d0e%22%2c%22Oid%22%3a%226972977d-2e62-4d80-8426-c2221155f801%22%7d

Seminario PRIN 2017: "Real and Complex Manifolds, Topology, and Holomorphic dynamics"

Van Tu Le, Tor Vergata. Dynamics of post-critically finite maps in higher dimension

Giovedì 9 Dicembre ore 16, Aula Dal Passo

Abstract:

In this talk, I will discuss the dynamics of post-critically finite, or PCF, endomorphisms in higher dimension. In dimension one, PCF rational maps are those with only periodic or preperiodic critical points. In higher dimension, PCF endomorphisms are endomorphisms of CP^k with only periodic or preperiodic critical hypersurfaces. In spite of being really well understood in dimension one, many classical results in dimension one remain unknown in higher dimension. I will focus on the progress of generalizing the following property of PCF rational maps : every nonzero multiplier of a PCF rational map has a modulus strictly bigger than 1. I will also discuss some active directions of research about PCF maps in higher dimension.