中科院数学与系统科学研究院
数学研究所
学术报告
多复变与复几何研讨班
报告人： Viet-Anh Nguyen教授（法国里尔大学）
题 目：Ergodic theory of singular holomorphic foliations
时 间：2024.02.26（星期一）下午1：30-3:00
地点：Zoom Meeting : 829 2334 3058 密码：378515
https://us06web.zoom.us/j/82923343058?pwd=iZfTO1FxD2kvTw8ZdP2aDUCai64Af2.1
摘 要：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 Poincaré 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.
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