Program in Holomorphic Dynamics, Laminations and Hyperbolic Geometry

AbstractAward：DMS-0555429首席研究员：Mikhail Lyubich该计划的主要重点是三维双曲几何和全纯动力学之间的相互作用。这两个领域在过去的30年里蓬勃发展，许多富有成果的交流丰富了它们。这两个领域都受到了重大的影响;双曲几何中的瑟斯顿几何化程序和复杂动力学中曼德布洛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，巩固这些最近的成就，并讨论他们打开进一步的方向。它还将触及一些活跃的相关领域：多变量的全纯动力学，层积和叶理，部分双曲动力学和Teichmuller流。 该方案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一个密集的学期的活动。在此期间，将举办一些研究生课程、小型课程和研讨会，以及三个关于该方案各种主题的讲习班。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。国家科学基金会的资金将用于支持希望参与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。http://www.fields.toronto.edu/programs/scientific/05-06/holodynamics/

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/