Workshops for Probabilistic Methods in Mathematical Physics

这是一项为2008- 2009年CRM（Centre de Recherches Mathematiques）数学物理中概率方法主题年计划的4个研讨会提供补充资金的提案，这些研讨会涉及与概率论密切相关的数学物理中心主题。所要求的资金是支付10名年轻参与者在美国大学的旅行和酒店费用，而没有为四个研讨会中的每一个提供NSF资助。这些讲习班得到协调，一些较年轻的参与者将被邀请参加不止一个讲习班。我们总共申请资助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，其重要性近年来才有所增加。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。另一个例子是Okounkov、Nekrasov、Kenyon和其他人最近的工作，他们使用随机分区来确定规范理论中模型的分区函数。另一个例子是布索-波尔钦斯基、道格拉斯等人将随机场应用于弦/M理论中的景观统计。时机已经成熟，可以通过一系列协调的研讨会和系列讲座，对概率方法及其应用进行为期一年的审查。更广泛的影响。该计划本质上是跨学科的，研讨会旨在将数学家和物理学家聚集在一起，研究密切相关（或相同的问题），但来自不同的研究传统。这种相互作用所产生的相互影响已经对当代数学产生了巨大的影响。许多当代物理学家反过来也深受数学发展的影响。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，并将使新一代人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.