Program in Holomorphic Dynamics, Laminations and Hyperbolic Geometry

Abstract Award: DMS-0555429 Principal Investigator: Mikhail Lyubich The main focus of the program will be the interaction between 3-dimensional hyperbolic geometry and holomorphic dynamics. These two fields have flourished through the past 30 years, with numerous fruitful 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 an intensive semester of activity in this area during the period January-May 2006. A number of graduate courses, mini-courses and seminars, as well as 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/