Workshops for Probabilistic Methods in Mathematical Physics

这是一项补充资金的建议，用于为CRM(数学研究中心)2008-2009年数学物理概率方法专题年计划的4个讲习班提供补充资金，这些讲习班涉及与概率论密切相关的数学物理的中心议题。申请的资金将用于支付一所美国大学10名年轻参与者的旅费和住宿费，而不是为四个研讨会的每个研讨会提供国家科学基金会的资助。讲习班是协调的，一些较年轻的参与者将被邀请参加一个以上的讲习班。总体而言，我们正在申请资助，以支持40名年轻参与者。概率论方法长期以来一直是物理学和数学的核心，近年来它们的重要性才有所增加。Schramm-Loewner演化的发展以及Lawler、Schramm、Smirnov、Werner等人在统计力学中的应用就是一个重要的例子。另一个是Okounkov，Nekrasov，Kenyon等人最近在规范理论中使用随机配分来确定模型配分函数的工作。另一类是Bousso-Polchinski、Douglas等人的随机场在弦/M理论中的景观统计中的应用。通过一系列协调一致的讲习班和系列讲座，对概率方法及其应用进行为期一年的审查的时机已经成熟。更广泛的影响。该计划本质上是跨学科的，而研讨会的设计目的是将从事密切相关(或相同问题)但来自不同研究传统的数学家和物理学家聚集在一起。这种互动的交融已经对当代数学产生了巨大的影响。作为回报，许多当代物理学家也受到了数学发展的高度影响。除了对现有研究人员的影响外，该计划还将带来许多研究生、博士后和其他年轻的研究人员，并将使新一代接触到这一重要领域。

This is a proposal for supplementary funding for 4 workshops of the 2008-9 thematic year program of Probabilistic Methods in Mathematical Physics at the CRM (Centre de Recherches Mathematiques), on central topics in mathematical physics which are closely connected to probability theory. The requested funding is to pay the travel and hotel expenses of 10 younger participants at a U.S. university without an NSF grant for each of the four workshops. The workshops are coordinated and some younger participants will be invited to more than one workshop. In total, we are applying for funding to support 40 younger participants. Probablilistic methods have long been central in physics and mathematics, and their significance has only increased in recent years. The development of the Schramm-Loewner evolution and its applications by Lawler, Schramm, Smirnov, Werner and others in statistical mechanics is one important example. Another is the recent work of Okounkov, Nekrasov, Kenyon and others on the use of random partitions to determine partition functions of models in gauge theory. Yet another are applications of random fields by Bousso-Polchinski, Douglas and others to landscape statistics in string/M theory. The time is ripe for a year long review of the probabalistic methods and their applications through a series ofcoordinated workshops and lecture series. Broader Impact. The program is by nature inter-discipinary, and the workshops are designed to bring together mathematicians and physicists working on closely related (or identical problems) but from differing research traditions. The cross-fertilization from this kind of interaction has already had an enormous impact on contemporary mathematics. Many contemporary physicists have in return been highly influenced by the mathematical developments. In addition to the impact on established researchers, the program will bring in many graduate students, post-docs and other young researches and will expose a new generation to this important field.