Workshops for Probabilistic Methods in Mathematical Physics

这是一份为2008- 2009年数学物理概率方法专题项目第二年的两个研讨会提供部分资金的提案。完整的计划，目前正在进行中，包括10个相互关联的研讨会，讨论数学物理的中心主题，这些主题与概率论密切相关。六个讲习班由NSF/DMS资助。两个车间。现已完成，由NSF基金PHY0757940资助，总金额为1万美元。目前的建议要求为其余两个讲习班提供相同的数额。申请的资金用于支付10名年轻的美国参与者的旅行和酒店费用；没有NSF资助的美国大学研究生、博士后或初级教员。智力优势：概率方法长期以来一直是物理和数学的核心，其重要性近年来才有所增加。劳勒、施拉姆、斯米尔诺夫、维尔纳等人对施拉姆-洛厄纳演化的发展及其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等人最近关于在规范理论中使用随机划分来确定模型的分配函数的工作。另一个例子是Bousso-Polchinski、Douglas等人将随机场应用于弦/M理论中的景观统计。发展主题的数量和速度都很大。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的时机已经成熟。更广泛的影响：该计划本质上是跨学科的，研讨会旨在汇集来自不同研究传统的数学家和物理学家，研究密切相关的问题。这种相互影响已经对当代数学产生了巨大的影响。反过来，许多当代物理学家也深受数学发展的影响。除了对现有研究人员的影响外，该项目还将吸引许多研究生、博士后和其他年轻研究人员，使新一代研究人员接触到这个快速发展的领域。

This is a proposal for partial funding of two workshops in the second year of the 2008-9 thematic year program of Probabilistic Methods in Mathematical Physics at the CRM (Centre de Recherches Mathematiques). The full program, now in progress, consists of 10 interrelated workshops on central topics in mathematical physics which are closely connected to probability theory. Six workshops are being funded by a grant from NSF/DMS. Two of the workshops. now complete, were funded a total of $10K by NSF grant PHY0757940. The current proposal asks for the same amount for the remaining two workshops. The requested funding is to pay the travel and hotel expenses of 10 younger US participants; graduate students, post-docs or junior faculty members at a U.S. university without an NSF grant. Intellectual Merit: 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 number and rate of developing topics is large. The time is ripe for a year long review of the probabalistic methods and their applications through a series of coordinated workshops and lecture series. Broader Impact: The program is by nature inter-discipinary, and the workshops are designed to bring together mathematicians and physicists from differing research traditions working on closely related problems . This cross-fertilization 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 researchers, exposing a new generation of researchers to this fast developing area.