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

几何、拓扑和数学物理中的概率方法专题学期

• 批准号: 1619617
• 负责人: Brian Rider
• 金额: $ 4.4万
• 依托单位: Temple University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2016
• 资助国家: 美国
• 起止时间: 2016-05-01 至 2019-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1619617&HistoricalAwards=false
• 关键词: Thematic; Semester; Probabilistic; Methods; Geometry

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

数学研究中心（CRM）将于2016年8月至12月在加拿大蒙特利尔组织一个关于几何、拓扑和数学物理中的概率方法的专题项目。该计划将是这一时期CRM的主要活动，由五个为期一周的密集讲习班组成。此外，还有三位顶尖数学家的系列讲座：Nalini Anantharaman（斯特拉斯堡大学），Yuval Peres（微软研究院）和Scott Sheffield（麻省理工学院）。研讨会之前将有高级研究生的预备讲座。在整个研讨会期间，CRM将接待许多长期访问者和博士后研究人员；该奖项为参加该计划的美国青年研究人员提供支持。概率方法在数学的许多领域中发挥着越来越重要的作用。CRM专题计划将涵盖广泛的主题，包括：度量流形的几何分析以及光谱理论和量子混沌的应用；量子引力中的随机度量几何及相关问题概率技术在偏微分方程中的应用随机域特征态定位；数论中的概率结果；随机简单复合体和三角空间的几何以及与几何群论、流形学习、拓扑统计和几何概率论的联系；三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kardarparisii - zhang方程）和可积离散模型的联系。该计划自然是跨学科的，重点是在概率论，几何分析，光谱理论，群论，拓扑学，几何和数学物理方面的研究人员之间的相互联系和思想的交叉交流。青年研究人员将有机会向这些领域的专家学习并与他们互动。http://www.crm.umontreal.ca/en/index.shtml