Travel Funding for International Conference (Groups-2003)

主要研究者：Vaughan F. Jones提案编号：DMS-0307231机构：加州大学伯克利分校技术摘要在意大利的盖塔举行的“2003年群体”会议的主要议题是离散群体。 它将侧重于：由有限自动机生成的群，Gromov意义上的双曲群，伯恩赛德群，李群中的格，中间增长群，以及李型离散群。关于这些群体的问题与下一节中提到的许多数学领域有关。会议期间讨论的主题将涉及增长的群体，子群的增长，性质（T），扩展和Ramanujan图，顺从性，非交换动力系统，随机行走的群体，正式语言，分支群体，自动机群体，分形群体和分形集，计算频谱的Hecke运营商，L2-不变量，有界上同调，和结构的格李群。 一个特别的重点将放在分支组，因为这次会议是专门为R。格里戈尔丘克在他50周年之际。 会议的主要议题当然属于群论，但它也密切相关的动力系统，遍历理论，几何度量空间，低维拓扑，离散数学，调和分析，算子代数，代表性的群体，和L2上同调。 计划在意大利的盖塔举行的"群--2003“会议旨在成为具有各种专业的数学家的聚会点，群论作为统一的基础。虽然以抽象代数为中心，但具有统计学，理论物理学以及纯数学广泛背景的参与者将尽可能多地强调数学的统一性，特别是群论。将慷慨地拨出时间供与会者进行非正式讨论和富有成果的交流。这些将包括国际知名的专家和研究生或希望进入快速发展领域的年轻研究人员。会议的记录将被编辑，并收集与会者的贡献。本次会议是恰如其分地致力于教授Grigorchuk为他的50岁生日，谁由他的众多贡献，各种不同领域的数学说明了本次会议的目标。

Principal Investigator: Vaughan F. JonesProposal Number: DMS-0307231Institution: University of California, BerkeleyTechnical AbstractThe main topic of the conference ``Groups--2003'' in Gaeta, Italy is Discrete Groups. It will concentrate on: groups generated by finite automata, hyperbolic groups in the sense of Gromov, Burnside groups, lattices in Lie groups, groups of intermediate growth, anddiscrete groups of Lie type. The questions concerning these groups are related to many areas of mathematics mentioned in the next section. The subjects discussed during the conference will be related to growth of groups, subgroup growth, property (T), expanders and Ramanujan graphs, amenability, non-commutative dynamical systems, random walks on groups, formal languages, branch groups, automata groups, fractal groups and fractal sets, computation of spectra of Hecke operators, L2-invariants, bounded cohomology, and the structure of lattices in Lie groups. A special emphasis will be put on branch groups, as this conference is dedicated to R. Grigorchuk on the occasion of his 50th anniversary. The main topic of the conference belongs of course to Group Theory, but it is also closely related to Dynamical Systems, Ergodic Theory, Geometry of Metric Spaces, Low-dimensional Topology, Discrete Mathematics, Harmonic Analysis, Operator Algebras,Representations of Groups, and L2 Cohomology. Non-Technical AbstractThe planned conference ``Groups--2003'' in Gaeta, Italy intends to be a meeting point for mathematicians with various specialties, with group theory serving as a unifying ground. While centered on abstract algebra, participants with a background from statistics, theoretical physics as well as the broad spectrum of pure mathematics will contribute talks that stress as much as possible the unifying nature of mathematics in general, and group theory in particular. Time will generously be alloted for informal discussion and fruitful exchanges between the participants. These will comprise both internationallyrenowned experts and graduate students or young researchers who wish to embark in the rapidly progressing field. Proceedings of the conference will be edited, and assemble contributions from the participants. This conference is fittingly dedicated to Professor Grigorchuk for his 50th birthday, who by his numerous contributions to various diverse fields of mathematics has illustrated the goals of this conference.