Conference on Quantum Integrable Systems, Conformal Field Theories and Stochastic Processes

量子可积系统、共形场论和随机过程会议

• 批准号: 1637087
• 负责人: Ivan Corwin
• 金额: $ 3万
• 依托单位: Columbia 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: 2016-07-01 至 2017-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1637087&HistoricalAwards=false
• 关键词: Conference; Quantum; Integrable; Systems; Conformal

This award will fund the conference "Quantum Integrable Systems, Conformal Field Theories and Stochastic Processes," which will be held from September 12-23, 2016, at the Institut d'Etudes Scientifique de Carges in Corsica, France. The conference website is https://indico.in2p3.fr/event/12461/. The topics of the conference are at the interface of mathematics and physics and are concerned with uncovering through exact calculation the universal behaviors of large, complex random systems. There are two main types of random systems -- those which are growing and those which have stabilized to a sort of equilibrium. The universal behaviors of each of these types of systems are rather different in characteristic. However, recent advances have indicated surprising connections between the behaviors of non-equilibrium and equilibrium systems. This conference will bring together experts in both areas with the aim of stimulating new advances and spark new connections. There is a strong emphasis on educating a new generation of researchers to appreciate and understand the broad cycle of ideas and motivations from both mathematics and physics in this area. Half of the lecturers will be mini-courses and the other half, research talks. This will benefit the many early-career researchers who will participate in the conference. The US participants funded by this award, most of whom are early-career researchers and graduate students, will benefit additionally by the opportunity to forge relations with their European colleagues. The organizers will actively encourage the participation of individuals from underrepresented groups in STEM, including women and minorities.Universality within and between complex random systems is a striking concept which has played a central role in the direction of research within probability, mathematical physics and statistical mechanics. Complementary to universality, is the exact description of the behaviors that are expected to be universal as well as the determination of which systems are meant to display them. In recent years there has been an immense amount of progress in the rigorous mathematical understanding of certain universal scaling limits in both equilibrium and non-equilibrium statistical physical systems. On the equilibrium side, critical scaling limits are often described in terms of conformal field theories, among which Liouville quantum gravity plays an important role. On the non-equilibrium side, systems like growth processes are described through the Kardar-Parisi-Zhang (KPZ) universality class. There is reason to believe that these two directions share many (as of yet) unexploited relationships. For instance, the field of quantum integrable systems was developed to study equilibrium systems, but has now found itself center stage in the KPZ universality class. Conversely, methods developed in stochastic partial differential equations for non-equilibrium systems have begun to make their way into constructive field theory. The purpose of this two-week conference is to bring together experts in these two areas and enable a lively exchange of ideas and methods through mini-courses and research talks.

该奖项将资助会议“量子可积系统，共形场理论和随机过程”，这将于2016年9月12日至23日在法国科西嘉的货物科学研究所举行。会议网址是https://indico.in2p3.fr/event/12461/。 会议的主题是在数学和物理的接口，并通过精确计算揭示大型复杂随机系统的普遍行为。随机系统主要有两种类型--增长的和稳定到某种平衡的。这些类型的系统中的每一种的普遍行为在特征上是相当不同的。然而，最近的进展表明非平衡和平衡系统的行为之间的惊人的联系。本次会议将汇集这两个领域的专家，旨在刺激新的进步并激发新的联系。有一个强烈的重视教育新一代的研究人员欣赏和理解的思想和动机从数学和物理在这一领域的广泛周期。 一半的讲师将是迷你课程，另一半是研究讲座。这将有利于许多早期的职业研究人员谁将参加会议。由该奖项资助的美国参与者，其中大多数是早期职业研究人员和研究生，将有机会与欧洲同事建立关系。组织者将积极鼓励来自代表性不足的群体的个人参与STEM，包括妇女和少数民族。复杂随机系统内部和之间的普遍性是一个引人注目的概念，在概率，数学物理和统计力学的研究方向中发挥了核心作用。 作为普遍性的补充，是对预期具有普遍性的行为的准确描述，以及确定哪些系统旨在显示它们。 近年来，对平衡和非平衡统计物理系统中某些普遍标度极限的严格数学理解取得了巨大的进展。 在平衡态方面，临界标度极限通常用共形场论来描述，其中刘维尔量子引力起着重要的作用。 在非平衡态方面，像增长过程这样的系统通过Kardar-Parisi-Zhang（KPZ）普适类来描述。 有理由相信，这两个方向有许多（迄今为止）未开发的关系。 例如，量子可积系统领域是为了研究平衡系统而发展起来的，但现在已经成为KPZ普适性类的中心舞台。 相反，在非平衡系统的随机偏微分方程中开发的方法已经开始进入建设性场论。 这个为期两周的会议的目的是将这两个领域的专家聚集在一起，并通过小型课程和研究会谈活跃地交流想法和方法。