Thematic Semester on Probabilistic Methods in Geometry, Topology, and Mathematical Physics

数学研究中心（CRM）将于2016年8月至12月期间在加拿大蒙特利尔举办一个关于几何，拓扑和数学物理中概率方法的主题计划。该方案将是客户关系管理在这一时期的主要活动，包括五个为期一周的密集讲习班。此外，还将有三位著名数学家的系列讲座：Nalini Anantharaman（斯特拉斯堡大学），Yuval Peres（微软研究院）和Scott谢菲尔德（麻省理工学院）。讲习班之前将为高级研究生举办预备讲座。许多长期访问者和博士后研究人员将在整个研讨会期间在CRM主持;该奖项为美国初级研究人员参与该计划提供支持。概率方法在数学的许多领域中起着越来越重要的作用。CRM专题计划将涵盖广泛的此类主题，包括：度量流形的几何分析及其在谱理论和量子混沌中的应用;随机度量的几何和量子引力中的相关问题;概率技术在偏微分方程中的应用;随机域中的本征态局部化;数论中的概率结果;随机单纯复形和三角剖分空间的几何学以及与几何群论、流形学习、拓扑统计和几何概率的联系; 3流形理论中的概率方法;随机增长问题和随机矩阵，以及它们与随机偏微分方程（如Kardar-Parisi-Zhang方程）和可积离散模型的联系。该计划自然是跨学科的，重点是研究人员在概率，几何分析，谱理论，群论，拓扑学，几何学和数学物理学之间的相互联系和思想交叉。年轻研究人员将获得向这些领域的专家学习和互动的绝佳机会。http://www.crm.umontreal.ca/en/index.shtml

The Centre de Recherches Mathematiques (CRM) will organize a Thematic Program on Probabilistic Methods in Geometry, Topology, and Mathematical Physics, held in Montreal, Canada, during the period of August to December, 2016. The Program, which will be the principal activity of the CRM in this period, is comprised of five intensive week-long workshops. In addition, there will be lecture series by three leading mathematicians: Nalini Anantharaman (Univ. Strasbourg), Yuval Peres (Microsoft Research), and Scott Sheffield (MIT). The workshops will be preceded by preparatory lectures for advanced graduate students. Numerous long-term visitors and postdoctoral researchers will be hosted at CRM throughout the seminar; this award provides support for junior US researchers to participate in the program. Probabilistic methods have played an increasingly important role in many areas of mathematics. The CRM Thematic Program will cover a broad range of such topics, including: geometric analysis on manifolds of metrics and applications to spectral theory and quantum chaos; geometry of random metrics and related problems in quantum gravity; applications of probabilistic techniques in partial differential equations; eigenstate localization in random domains; probabilistic results in number theory; random simplicial complexes and geometry of spaces of triangulations and connections to geometric group theory, manifold learning, topological statistics, and geometric probability; probabilistic methods in 3-manifold theory; random growth problems and random matrices, and their connections to stochastic partial differential equations (such as the Kardar-Parisi-Zhang equation) and to integrable discrete models. The program is naturally interdisciplinary, with an emphasis on interconnections and cross fertilization of ideas between researchers working in probability, geometric analysis, spectral theory, group theory, topology, geometry, and mathematical physics. Young researchers will be provided with an excellent opportunity to learn from and interact with experts in these fields. http://www.crm.umontreal.ca/en/index.shtml