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

关于KPZ普遍性和指导聚合物的学期将于2017年2月1日至7月31日在法国Luminy的Center International De Rencontres Mathematiques举行。该计划的目的是将来自世界各地的领先研究人员汇集在一起​​，以增强我们对KPZ通用的理解。这是过去十年中统计力学和数学物理学中最活跃的领域之一，它重点是研究高度相关的随机系统的极端。值得注意的是，不管正在考虑的特定系统如何，控制极端的统计数据似乎是普遍的，尽管到目前为止，这仅是针对非常特定的系统才能理解的。该计划的主要重点是了解普遍性背后的统一机制，这是由有指示聚合物模型的示例所激发的。这将以跨学科的方式使用统计力学，概率理论，动力学系统和部分微分方程的思想来完成。学期的智力优点在于它的潜力是在数学的不同领域建立思想的交叉剥夺，并将这些思想与理论物理和其他科学领域联系起来。将通过跨学科的这种思想交流以及培训新一代学生在这一重要领域进行工作。除了实现领先的研究人员之间的长期合作外，该学期还将允许在KPZ中的定性方法（2017年4月24-27，2017年4月24-27，2017年4月24-27日）和2017年的环境中，将新成果传播出来。统计力学和数学物理学随机结构的研究学校（2017年3月6日至10日）旨在将研究生和其他初级研究人员介绍到这个令人兴奋的新领域。该提案的资金将使美国的学生和初级研究人员参与这些计划。会议网站：Khanin-Shlosman.weebly.com