CBMS Conference: Dyson-Schwinger Equations, Topological Expansions, and Random Matrices

CBMS 会议：Dyson-Schwinger 方程、拓扑展开式和随机矩阵

• 批准号: 1642595
• 负责人: Ivan Corwin
• 金额: $ 3.78万
• 依托单位: Columbia University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2017
• 资助国家: 美国
• 起止时间: 2017-07-01 至 2018-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1642595&HistoricalAwards=false
• 关键词: CBMS; Conference; Dyson; Schwinger; Equations

This award provides support for the CBMS conference "Dyson-Schwinger Equations, Topological Expansions, and Random Matrices," which will run from August 28 to September 1, 2017 at Columbia University in New York City. The conference features a series of ten lectures by mathematician Alice Guionnet. Probability, as a field, seeks to understand how large, complex random systems manifest deterministic behaviors, and universal fluctuations around them. Matrices are fundamental objects in mathematics and all of science -- they encode transformations of space, descriptions of atoms in physics, chains of chemical reactions and probabilities in chemistry, and series of observations in experimental sciences, and they are vital in signal processing. In many applications, there is noise present in the system under study, and the associated matrices end up having structured but random entries. The fundamental challenge becomes to understand the effect of noise on these structures. How does it change the key properties of these objects, and how can statistical methods be developed to separate the signal from the noise? The principal lecture series will report on some of the most exciting new advances in tackling these types of questions. The meeting also will include presentations by other experts in the subject area. There will also be daily tutorials and problem sessions, with lecture notes provided in advance to help students prepare adequately.Understanding the large-dimension asymptotics of random matrices or related models such as random tilings has been of great interest for the last twenty years within probability, mathematical physics, and statistical mechanics. Because such models are highly correlated, classical methods based on independent variables fail. Special cases have been studied in detail thanks to specific forms of the laws, such as determinantal laws. These lectures will discuss a general class of models using the so-called Dyson-Schwinger equations and generalizations. The ten lectures cover the following subjects: law of large numbers in random matrices and concentration of measure; central limit theorem in the one-cut case; generalization to the discrete setting of tiling models; topological expansions for large-N asymptotics of partition functions; and generalization to several-cut models. Additional talks will be presented by Charles Bordenave (University of Toulouse), Gaetan Borot (Max Planck Institute for Mathematics, Bonn), Paul Bourgade (New York University), Vadim Gorin (Massachusetts Institute of Technology), and Antti Knowles (ETH Zurich).The website for this conference is: http://www.math.columbia.edu/department/probability/seminar/Guionnet.html

该奖项为CBMS会议“ Dyson-Schwinger方程，拓扑扩展和随机矩阵”提供了支持，该会议将于2017年8月28日至9月1日在纽约市的哥伦比亚大学举行。 该会议的特色是数学家爱丽丝·吉恩内特（Alice Guionnet）的一系列十个演讲。作为一个领域的概率，试图了解大型，复杂的随机系统如何表现出确定性行为和周围的普遍波动。矩阵是数学和所有科学中的基本对象 - 它们编码空间的转换，物理学的描述，化学反应和化学概率的链以及实验科学中的一系列观察结果，它们对于信号处理至关重要。在许多应用中，正在研究的系统中存在噪声，并且相关矩阵最终具有结构性但随机的条目。基本挑战成为了解噪声对这些结构的影响。它如何改变这些对象的关键属性，如何开发统计方法以将信号与噪声分开？主要讲座系列将报道解决这类问题的一些最令人兴奋的新进步。会议还将包括主题领域其他专家的演讲。 还将每天都有教程和问题会议，并提前提供了讲义，以帮助学生充分准备。了解随机矩阵的大差异渐近造型或相关模型（例如随机块状）在过去的五十年内对概率，数学物理学和统计机制引起了极大的兴趣。由于此类模型高度相关，因此基于自变量的经典方法失败。由于特定形式的法律，例如决定性法律，已经对特殊案例进行了详细研究。这些讲座将使用所谓的Dyson-Schwinger方程和概括讨论一类通用模型。十个讲座涵盖以下主题：随机矩阵中的大量定律和度量浓度；在一个切割情况下，中央限制定理；对平铺模型的离散设置的概括；分区函数的大N渐进性拓扑扩展；并概括多个切割模型。 查尔斯·博德纳夫（Toulouse of Toulouse），Gaetan Borot（Max Planck数学研究所，波恩），Paul Bourgade（纽约大学），Vadim Gorin（马萨诸塞州技术研究所）和本次会议的网站。 http://www.math.columbia.edu/department/probiable/seminar/guionnet.html