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

该奖项将资助将于2016年9月12-23日在法国科西嘉岛卡日学院举行的“量子可积系统、共形场理论和随机过程”会议。会议网址为：https://indico.in2p3.fr/event/12461/.会议的主题是数学和物理的交界点，并关注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--一种是增长的，另一种是已经稳定到某种平衡的。每一种类型的系统的通用行为在特征上都有很大的不同。然而，最近的进展表明，非平衡系统和平衡系统的行为之间存在令人惊讶的联系。这次会议将汇聚这两个领域的专家，目的是促进新的进展和建立新的联系。我们非常重视培养新一代的研究人员，让他们欣赏和理解这一领域中数学和物理的思想和动机的广泛循环。一半的讲师将是迷你课程，另一半将是研究讲座。这将使许多将参加会议的早期研究人员受益。该奖项资助的美国参与者大多是职业生涯早期的研究人员和研究生，他们还将受益于与欧洲同行建立关系的机会。组织者将积极鼓励代表不足的群体中的个人参加STEM，包括妇女和少数民族。复杂随机系统内部和之间的共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。对普遍性的补充是对预期具有普遍性的行为的准确描述，以及确定哪些系统将显示这些行为。近年来，在对平衡和非平衡统计物理系统中某些普适标度极限的严格数学理解方面取得了巨大的进展。在平衡态方面，临界标度极限通常用共形场理论来描述，其中Liouville量子引力起着重要的作用。在非平衡方面，通过Kardar-Parisi-Zhang(KPZ)普适性类来描述类似增长过程的系统。有理由相信，这两个方向有许多(截至目前)尚未开发的关系。例如，量子可积系统领域的发展是为了研究平衡系统，但现在发现自己处于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组中发展起来的方法已经开始进入构造场理论。这次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讲座来活跃地交流想法和方法。

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.