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

NSF/CBMS数学科学区域会议，分形理论中的遍历方法，2011年6月18日至23日分形几何研究欧几里得空间的闭紧子集。通常的概念是一个整数的维数是取代豪斯多夫维数。分形在复杂动力学、数学物理、丢番图逼近等数学领域中发挥着重要作用。遍历理论研究了一个动力系统（一个具有同胚的紧致度量空间）在长时间运行时的行为。在一定的条件下（遍历性），函数的时间平均收敛于其空间平均。遍历理论广泛应用于数学的许多领域，如组合数论，数学物理，李群等。这次CBMS会议的主要重点是发展遍历方法来解决几何，分析，概率和组合问题，呼吁本科生和研究生注意分析师和几何学家共同感兴趣的一些主题，并在这些领域提供基本的指导，强调所涉及的基本遍历思想。特别注意将提请应用遍历理论的分形几何（问题涉及行为的分形集，措施与统一缩放的风景，CP过程，拉姆齐型的结果）。对这门学科的兴趣是基于它的重要性，以实现在解决有关分形几何和加法组合学的不同问题的进展。希勒尔Furstenberg是众所周知的，他的应用概率和遍历方法的其他领域的数学，包括数论和李群。他的演讲是真正的杰作，绝对独立，任何人都可以访问-从专家到研究生和本科生。

NSF/CBMS Regional Conference in the Mathematical Sciences, Ergodic Methods in the Theory of Fractals, June 18-23, 2011Fractal 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.