Conference Proposal: Semester on KPZ Universality and Directed Polymers

会议提案：KPZ 通用性和定向聚合物学期

• 批准号: 1656377
• 负责人: Thomas Alberts
• 金额: $ 4.95万
• 依托单位: University of Utah
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2017
• 资助国家: 美国
• 起止时间: 2017-01-01 至 2017-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1656377&HistoricalAwards=false
• 关键词: Conference; Proposal; Semester; KPZ; Universality

The Semester on KPZ Universality and Directed Polymers will be hosted at the Centre International de Rencontres Mathematiques, in Luminy, France, from February 1 to July 31, 2017. The purpose of the programme is to bring together leading researchers from around the world to strengthen our understanding of KPZ universality. This is one of the most active areas of statistical mechanics and mathematical physics in the last ten years that is focused on studying the extremes of highly correlated random systems. Remarkably, the statistics governing the extremes appear to be universal regardless of the particular system under consideration, although thus far this has only been understood for very specific systems. The main focus of the program is to understand the unifying mechanism behind the universality, motivated by examples from directed polymer models. This will be done in an interdisciplinary manner using ideas from statistical mechanics, probability theory, dynamical systems, and partial differential equations. The intellectual merit of the semester lies in its potential to establish a cross-fertilization of ideas within different areas of mathematics and connect these ideas with theoretical physics and other fields of science. Broader impact will be realized via this exchange of ideas across disciplines and through the training of a new generation of students to carry on the work in this important field.In addition to enabling long-term collaborations between leading researchers, the semester will allow for the dissemination of new results with a conference on Qualitative Methods in KPZ Universality (April 24-27, 2017) and a small groups meeting on Random Walks in Random Environments (March 13-17, 2017).There will also be a research school on Random Structures in Statistical Mechanics and Mathematical Physics (March 6-10, 2017) aimed at introducing graduate students and other junior researchers to this exciting new field. Funds from this proposal will enable the participation of United States based students and junior researchers in these programs. Conference website: khanin-shlosman.weebly.com

KPZ普遍性和定向聚合物学期将于2017年2月1日至7月31日在法国卢明的国际Rencontres数学中心举行。该计划的目的是汇集来自世界各地的领先研究人员，以加强我们对KPZ普遍性的理解。这是近十年来统计力学和数学物理中研究高度相关随机系统的极值问题最为活跃的领域之一。值得注意的是，控制极端的统计数据似乎是普遍的，而不考虑所考虑的特定系统，尽管到目前为止，这只被理解为非常具体的系统。该计划的主要重点是了解普遍性背后的统一机制，由定向聚合物模型的例子驱动。这将以跨学科的方式完成，使用统计力学，概率论，动力系统和偏微分方程的思想。本学期的智力价值在于它有可能在数学的不同领域建立思想的交叉受精，并将这些思想与理论物理和其他科学领域联系起来。通过跨学科的思想交流和培养新一代学生在这一重要领域开展工作，将实现更广泛的影响。除了促进主要研究人员之间的长期合作外，本学期还将通过KPZ普世性定性方法会议（2017年4月24日至27日）和随机环境中的随机漫步小组会议（2017年3月13日至17日）传播新结果。此外，统计力学和数学物理中的随机结构研究学院（2017年3月6日至10日）旨在向研究生和其他初级研究人员介绍这一令人兴奋的新领域。这项提案提供的资金将使在美国的学生和初级研究人员能够参与这些项目。会议网站：khanin-shlosman.weebly.com