Speaker: Zhangchi Chen（East China Normal University）
Time: 10:00-11:00, Jul 11, 2025
Room: room 1124, Material Science Research Building (Section C)
Holomorphic foliations are geometric structures to foliate high dimensional complex manifolds with low dimensional ones (called leaves). The key problem in this area is to study the density and the distribution of leaves. Fornaess-Dinh-Nguyen-Sibony proved that in compact Kahler surfaces, foliations with only hyperbolic singularities admits unique ergodicity. In particular, if the foliation does not direct any positive closed currents, then there is a unique (up to scaling) positive harmonic current directed by it. As a consequence, each leaf is dense and has the same distribution in the sense of Nevanlinna currents.
In this talk I will introduce the basic concepts about holomorphic foliations, hyperbolic singularities, harmonic currents. I will review the unique ergodicity, and talk about my result on the Lelong number of directed harmonic currents. Finally, I will talk about some open problems.
