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“量子整合系统，共形领域理论和随机过程”，该奖项将于2016年9月12日至23日在法国科西嘉岛举行。会议网站是https://indico.in2p3.fr/event/12461/。 会议的主题是在数学和物理学的界面上，并且与通过精确计算大型，复杂的随机系统的普遍行为有关。随机系统有两种主要类型 - 那些正在生长的系统，而那些已经稳定在某种平衡的系统中。这些类型的系统的普遍行为在特征上都大不相同。但是，最近的进步表明，非平衡和平衡系统的行为之间存在令人惊讶的联系。这次会议将在这两个领域汇集专家，以刺激新的进步并引发新的联系。人们非常重视教育新一代研究人员，以欣赏和理解该领域数学和物理学的思想和动机的广泛循环。 一半的讲师将是小型演出，另一半是研究谈判。这将使许多将参加会议的早期研究人员受益。由该奖项资助的美国参与者，其中大多数是早期的研究人员和研究生，还将受益于与欧洲同事建立关系的机会。组织者将积极鼓励来自代表性不足群体的个人参与，包括妇女和少数群体。复杂的随机系统内部和之间的宇宙性是一个引人注目的概念，它在概率，数学物理学和统计机制的研究方向中起着核心作用。 对普遍性的补充是对期望是普遍的行为的确切描述，以及确定哪些系统旨在显示它们的行为。 近年来，在平衡和非平衡统计物理系统中对某些通用缩放限制的严格数学理解中取得了巨大进展。 在平衡方面，临界尺度限制通常是通过共形场理论来描述的，其中liouville量子重力起着重要作用。 在非平衡方面，通过Kardar-Parisi-Zhang（KPZ）通用类别描述了诸如生长过程之类的系统。 有理由相信这两个方向共享许多（迄今为止）尚未开发的关系。 例如，开发了量子整合系统的领域来研究平衡系统，但现在发现自己在KPZ通用类别中的中心阶段。 相反，在非平衡系统的随机部分微分方程中开发的方法已开始进入建设性领域理论。 这个为期两周的会议的目的是将这两个领域的专家汇集在一起​​，并通过迷你巡回演唱会和研究演讲来激动人心地交流思想和方法。