Program in Holomorphic Dynamics, Laminations and Hyperbolic Geometry

全纯动力学、叠片和双曲几何课程

• 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

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：DMS-0555429首席研究员：米哈伊尔·柳比希该计划的主要重点将是三维双曲几何和全纯动力学之间的相互作用。在过去的30年里，这两个领域蓬勃发展，无数富有成效的交流丰富了两个领域。这两个领域都受到了重大猜想的严重影响：双曲几何中的瑟斯顿几何化方案和复杂动力学中曼德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振奋的突破。该计划提供了一个机会来巩固这些最新的成就，并讨论它们所开辟的进一步方向。它还将涉及一些活跃的相关领域：多变量的全纯动力学、层理和层理、部分双曲动力学和泰希米勒流。该计划将在菲尔兹学院进行，该学院将在2006年1月至5月期间在这一领域开展密集学期的活动。在此期间，将举办一些研究生课程、小型课程和研讨会，以及关于该方案不同主题的三个讲习班。它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。美国国家科学基金会的资金将用于支持希望参加这项活动的美国数学家，主要是没有其他支持来源的年轻数学家。该计划的网站是http://www.fields.toronto.edu/programs/scientific/05-06/holodynamics/