Program in Holomorphic Dynamics, Laminations and Hyperbolic Geometry

全纯动力学、叠片和双曲几何课程

基本信息

批准号：
0555429
负责人：
Mikhail Lyubich
金额：
$ 4.5万
依托单位：
SUNY at Stony Brook
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2006
资助国家：
美国
起止时间：
2006-02-15 至 2007-01-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=0555429&HistoricalAwards=false
关键词：
Program Holomorphic Dynamics Laminations Hyperbolic

项目摘要

AbstractAward: DMS-0555429Principal Investigator: Mikhail LyubichThe main focus of the program will be the interaction between3-dimensional hyperbolic geometry and holomorphic dynamics. These two fields have flourished through the past 30 years, with numerousfruitful exchanges that have enriched both of them. Both fields have been heavily influenced by major conjectures; the Thurston Geometrization Program in hyperbolic geometry and investigation of the intricate structure of the Mandelbrot set in complex dynamics. Recent years have witnessed many exciting breakthroughs in the both fields. The program provides an opportunity to consolidate these recent achievements and to discuss further directions they open. It will also touch on a number of active related fields: holomorphic dynamics in several variables, laminations and foliations, partially hyperbolic dynamics, and Teichmuller flow. The program will take place at the Fields Institute, which is mounting anintensive semester of activity in this area during the period January-May2006. A number of graduate courses, mini-courses and seminars, as wellas three Workshops on various themes of the program will be carried out during that time. They will be largely directed towards young researches who will have an opportunity to learn about most recent events in the field. The NSF funding will be used to support American mathematicians who wish to participate in this activity, principally young mathematicians without other sources of support.The program Web site is http://www.fields.toronto.edu/programs/scientific/05-06/holodynamics/

摘要奖项：DMS-0555429 首席研究员：Mikhail Lyubich 该项目的主要焦点将是三维双曲几何与全纯动力学之间的相互作用。 30年来，这两个领域蓬勃发展，交流丰硕，成果丰硕。这两个领域都深受重大猜想的影响；双曲几何中的瑟斯顿几何化程序以及复杂动力学中曼德尔布罗特集的复杂结构的研究。近年来，这两个领域都取得了许多令人兴奋的突破。该计划提供了一个机会来巩固这些最近的成就并讨论它们开辟的进一步方向。它还将涉及许多活跃的相关领域：多个变量的全纯动力学、层状结构和叶状结构、部分双曲动力学和 Teichmuller 流。该项目将在菲尔兹研究所进行，该研究所将在 2006 年 1 月至 5 月期间在这一领域开展密集的学期活动。在此期间将举办一些研究生课程、迷你课程和研讨会，以及三个关于该计划不同主题的研讨会。他们将主要针对年轻的研究人员，他们将有机会了解该领域的最新事件。 NSF的资金将用于支持希望参加这项活动的美国数学家，主要是没有其他来源支持的年轻数学家。该计划的网站是http://www.fields.toronto.edu/programs/scientific/05- 06/全息动力学/