Conference Proposal: Semester on KPZ Universality and Directed Polymers

关于KPZ普适性和定向聚合物的学期将于2017年2月1日至7月31日在法国鲁米尼的国际伦孔特数学中心举行。该方案的目的是将来自世界各地的顶尖研究人员聚集在一起，以加强我们对KPZ普遍性的了解。这是过去十年来统计力学和数学物理中最活跃的领域之一，其重点是研究高度相关的随机系统的极值。值得注意的是，无论所考虑的特定系统如何，管理极端情况的统计数据似乎都是通用的，尽管到目前为止，这一点只被理解为非常具体的系统。该计划的主要重点是理解普遍性背后的统一机制，其动机来自定向聚合物模型的例子。这将利用统计力学、概率论、动力系统和偏微分方程式的思想以跨学科的方式完成。这学期的智力价值在于它有可能在不同的数学领域建立思想的交叉培养，并将这些思想与理论物理和其他科学领域联系起来。通过这种跨学科的思想交流和通过培训新一代学生从事这一重要领域的工作，将产生更广泛的影响。除了促进领先研究人员之间的长期合作外，本学期还将允许通过KPZ普遍性定性方法会议(2017年4月24日至27日)和关于随机环境中的随机行走的小组会议(2017年3月13日至17日)传播新成果。还将设立统计力学和数学物理随机结构研究学校(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。这项提案的资金将使美国的学生和初级研究人员能够参与这些项目。会议网址：khanin-shlosman.webly.com

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