The ergodicity conjecture in dimension 3

：Raul Ures（南方科技大学）
：2022-12-30 15:00
：腾讯会议ID：897-810-113（无密码）

报告人：Raul Ures（南方科技大学）

时  间：12月30日下午15:00-16:30

地  点：腾讯会议ID：897-810-113（无密码）

内容摘要:

A diffeomorphism f is partially hyperbolic if its tangent bundle splits into three invariant bundles: one is contracted (stable), one is expanded (unstable), and the third one has an intermediate behavior (center). For conservative f, there is a famous conjecture of Pugh and Shub that says that an open dense diffeomorphism of these diffeomorphisms is ergodic. This conjecture has already been proved by Hertz-Hertz-Ures (HHU) if the center dimension is 1. In the case that the manifold has dimension 3, the three bundles have dimension 1, and then we can ask if we can go further in describing the set of ergodic diffeomorphisms. About fifteen years ago HHU conjectured that, in dimension 3, all partially hyperbolic diffeomorphisms are ergodic except for some particular cases of ambient manifolds (which, in particular, have (virtually) solvable fundamental group). In this talk we plan to present the advances obtained in this conjecture, with emphasis on recent times where the study of this conjecture has been especially active.

个人简介：

Raul Ures is an Uruguayan mathematician working in dynamical systems and ergodic theory. He did his undergraduate studies in Uruguay and obtained his PhD at IMPA, Brazil. After that he developed most of his academic career in Uruguay until 2016 when he joined SUSTech. He is currently a professor at SUSTech and is an A-level researcher in the Peacock program of Shenzhen City. He has published research papers in Acta Math., Invent. Math., Duke Math. J., etc.

 

联系人：吴伟胜