Geometries at SISSA -- Simone Diverio

[Antonio Lerario]

Dear All,

this is to announce our next seminar from the series "Geometries at SISSA".

The purpose of this series is to present topics in modern geometry in a way
that is accessible to a broad audience, in a colloquium style seminar.

After the seminar we will also go to get dinner together, please sign up
here <https://forms.gle/JXpufpJ3c8m3oaFu7>.
Everyone is welcome to join!

Our speaker will be Simone Diverio
<https://sites.google.com/a/uniroma1.it/simonediverio/>
<https://sites.google.com/a/uniroma1.it/simonediverio/>(Sapienza).

-----
Speaker: Simone Diverio (Sapienza)
Title: Recent progress on Lang's conjecture

Time: April 6, 5pm (Rome time)
Venue: room 133
>From remote at this link https://sissa-it.zoom.us/j/86574806499

Abstract: A compact complex manifold is said to be Kobayashi hyperbolic if
every homomorphic map from the complex plane to it is constant; it is said
to be of general type if the global holomorphic sections of (a power of)
its canonical bundle define a birational map.
Lang's conjecture (dating back 1986) connects these two properties and
claims that a projective algebraic manifold is Kobayashi hyperbolic if and
only if all its subvarieties (including itself) are of general type.
It is a quite subtle claim, which has deep connections also with complex
differential geometry and arithmetic geometry.
I will try to explain what motivates the conjecture, which is still
completely open in its full generality, and to present some recent progress
on the necessity condition.