Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	Viet-Anh Nguyen 教授,法国里尔大学
Inviter:
Title:	Ergodic theory of singular holomorphic foliations
Language:	Chinese
Time & Venue:	2024.02.26 13:30-15:00 Zoom Meeting : 829 2334 3058 密码：378515
Abstract:	This lecture discusses recent results as well as new perspectives in the ergodic theory for hyperbolic Riemann surface laminations, with an emphasis on singular holomorphic foliations by curves. The central notions of these developments are directed positive harmonic currents, multiplicative cocycles and leafwise Poincar metric. We deal with Geometric Birkhoff Ergodic Theorem and Unique Ergodicity Theorems. Applications of these theorems are also given. In particular, we define and study the canonical Lyapunov exponents for a large family of singular holomorphic foliations on compact projective surfaces. Topological and algebro-geometric interpretations of these characteristic numbers are also treated. These results highlight the strong similarity as well as the fundamental differences between the ergodic theory of maps and that of Riemann surface laminations.