NSF/CBMS Research Conference in the Mathematical Sciences - "Ergodic Methods in the Theory of Fractals" - "6/18/11 - 06/23/11"

Kent State University, Kent OH

Investigators

Abstract

NSF/CBMS Regional Conference in the Mathematical Sciences, Ergodic Methods in the Theory of Fractals, June 18-23, 2011 Fractal geometry studies closed compact subsets of a Euclidean space. The usual notion of a dimension which is an integer number is replaced by Hausdorff dimension. Fractals play an important role in complex dynamics, mathematical physics, Diophantine approximation and many other areas of mathematics. Ergodic theory studies the behavior of a dynamical system (a compact metric space with a homeomorphism) when it is allowed to run for a long time. Under certain conditions (ergodicity), the time average of a function converges to its space average. Ergodic theory is widely used in many areas of mathematics such as combinatorial number theory, mathematical physics, Lie groups and others. The main focus of this CBMS conference is to develop Ergodic methods to solve geometric, analytic, probabilistic and combinatorial problems, to call attention of undergraduate and graduate students to a number of topics of common interest to analysts and geometers, and to provide basic instruction in these areas with an emphasis on the fundamental ergodic ideas involved. Particular attention will be drawn to applications of Ergodic Theory to Fractal Geometry (questions involving behavior of fractal sets, measures with uniform scaling scenery, CP processes, Ramsey type results). The interest in the subject is based upon its importance in order to achieve progress in solving different problems related to the Fractal geometry and additive combinatorics. Hillel Furstenberg is widely known for his application of probabilistic and ergodic methods to other areas of mathematics, including number theory and Lie groups. His talks are true masterpieces that are absolutely self-contained and accessible to anyone - from specialists to graduate and undergraduate students.