On Dynamics of Holomorphic foliations in CP2.
Nessim Sibony, Université de Paris-Sud, Orsay, France

Global properties of holomorphic foliations in CP2 are
poorly understood. It is still unknown wether every
leave clusters at a singular point. The origin of the
subject are attempts to count the number of cycles for
polynomial vector fields in the real plane, hence to
consider the complexification. In this talk we will
discuss unique ergodicty for such foliations. The main
result is that for generic foliations of degree d, there
is a unique positive harmonic current of mass one directed
by the foliation. This implies that appropriate averages
on leaves have a unique limit, independent of the leave
and of the averaging process. This is joint work with
with J.E Fornaess.

Colloquium, Department of Mathematics, Rice University
January 24, 2008, 4-5PM, HB 227


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