|
and
|
|
The field of holomorphic dynamics underwent rapid development,
influencing (and influenced by) algebraic geometry. The methods of
ergodic theory were especially useful to treat discrete group acting on
complex manifolds. This is where holomorphic dynamics meets hyperbolic
geometry which is another theme of the meeting. Discrete group actions
on complex hyperbolic spaces produce many interesting examples of
complex manifolds and give important insights into the geometry of
projective manifolds of general type. Hyperbolic manifolds and
manifolds of general type are the arena of some of the most fascinating
and mysterious conjectures of algebraic geometry: the conjectures of
Green-Griffiths and Lang that relate the complex geometry of a manifold
(in particular, the Kobayashi pseudometric) with its algebraic and
number-theoretic properties. In this direction, a number of fascinating
results were obtained by Bogomolov and McQuillan, relating the
Green-Griffiths conjectures with the geometry of holomorphic foliations.
The theory of holomorphic
foliations is where complex dynamics meets algebraic geometry: in the
last 10 years, the theory of holomorphic foliations became crucially
important, with many applications to complex algebraic geometry and
classification theorems. We plan to treat the three themes of our
conference (complex dynamics, holomorphic foliations and hyperbolic
algebraic geometry) as a single theory; while technically separated,
they are connected on a deeper level and interwind many aspects of
differential geometry, algebraic geometry, and complex analysis.