Conference on Recent Developments in von Neumann Algebras; May 14-17, 2003; Los Angeles, CA

冯诺依曼代数最新发展会议；

• 批准号: 0315442
• 负责人: Sorin Popa
• 金额: $ 2.52万
• 依托单位: University of California-Los Angeles
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2003
• 资助国家: 美国
• 起止时间: 2003-04-01 至 2004-03-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0315442&HistoricalAwards=false
• 关键词: Conference; Recent; Developments; von; Neumann

AbstractShlyakhtenkoShlyakhtenko will study classes of operator algebras arising in connectionwith Voiculescu's free probability theory. The main emphasis of thisresearch is placed on the study of operator-valued free randomvariables and operator algebras that they generate. Analysis of thesevon Neumann algebras is intimately tied with the goal ofclassification of free Araki-Woods factors, which are free probabilityanalogs of ITPFI type III factors. Such analysis is also importantfor understanding of subfactors and automorphisms of amalgamated freeproduct algebras. One of the goals of the present research is todevelop free entropy-based techniques for dealing with operator-valuedrandom variables.Free probability theory is a highly non-commutative parallel to basicprobability theory. Matrix-valued random variables (such as randommatrices) naturally fit in the non-commutative probability framework;the asymptotic behavior of large random matrices is well-modeled bymatrix-valued free random variables. Applications are in mathematicsto the theory of operator algebras, subfactors, ergodic theory, aswell as the theory of random matrices, which have connections withcertain physical models.

Abstractshlyakhtenkhtenkoshlyakhtenko将研究与Voiculescu的自由概率理论相关的操作员代数的类别。 本研究的主要重点放在其产生的操作员可价值的自由随机变量和操作符代数的研究上。 对这些诺伊曼代数的分析与自由araki-woods因子的分类息息相关，这是ITPFI III型因子的自由概率分析。 这种分析对于理解合并的自由状学代数的亚因子和自身形态的理解也很重要。 本研究的目标之一是用于处理操作员 - valueDrandom变量的基于自由熵的技术。免费概率理论是一种与基本探针理论相似的高度不相同的。 矩阵值随机变量（例如randommatrices）自然拟合在非交通概率框架中；大型随机矩阵的渐近行为被amtrix-valued的自由随机变量很好地模块化。 在数学中，应用程序代数，子因子，厄法德理论，以及随机矩阵的理论，与随机矩阵的理论相同，这些理论与确定的物理模型具有连接。