Conference on Recent Mathematical Advances in Classical, Quantum and Statistical Mechanics

“经典、量子和统计力学的最新数学进展”会议将于2013年3月8-9日在弗吉尼亚大学举行。本次会议的目标是对数学分析领域的一些主要最新成果进行调查，该领域研究在各种环境下具有大或无限多个自由度的物理系统的演化，同时强调这些环境中常见的思想和技术。本次会议的主题是当代数学物理学中最活跃的主题之一。会议将汇集世界领先的专家在偏微分方程的KAM理论，泛函分析中的重排列不等式，安德森局域化，极化子系统的研究和耦合非谐振子的非平衡统计力学等主题。会议将为传播该领域的最新成果和方法提供一个场所，并将促进在这些重要议题方面取得进一步进展。这次会议的一个重要组成部分是教育，旨在传播经典力学、量子力学和统计力学的最新进展。重点将放在鼓励高级和初级研究人员之间的互动。将特别努力邀请和支持来自代表性不足群体的研究生、博士后和数学家。对具有无限个自由度的系统的演化的研究在现代科学中是普遍存在的。在有关经典力学的情况下，一个典型的例子是流体的演化，其中自由度基本上对应于流体在空间中某一点的速度。由于有无穷多个这样的点，我们观察的是一个具有无穷多个相互作用自由度的复杂系统。这就产生了非线性偏微分方程，它在诸如天气预报模型等大量应用中发挥了重要作用。在量子情况下，这种系统的例子是极化子系统，它描述了离子晶体（类似于普通盐的结构）中粒子的运动。另一个以安德森局域化的名义研究的例子与量子粒子与随机介质相互作用的运动有关。后者被认为是模拟，例如，半导体中的杂质。最后，统计力学是第三种状态，其中具有无限多个自由度的系统是非常活跃的研究对象，特别是在非平衡状态下。这一领域的数学挑战的一个例子是理解热和电的传导，不是通过特别的现象学描述，而是通过从第一原理的推导：微观层面上的经典或量子力学的基本定律。

The conference "Recent Mathematical Advances in Classical, Quantum and Statistical Mechanics" will be held at the University of Virginia on March 8-9, 2013. The goal of the conference is to present a survey of some of the major recent results in the area of mathematical analysis which studies the evolution of physical systems with large or infinite number of degrees of freedom in a variety of settings while emphasizing ideas and techniques which are common to these settings. The subject of this conference is one of the most active in contemporary mathematical physics. The conference will bring together leading world-experts in such topics as KAM theory for partial differential equations, rearrangement inequalities in functional analysis, Anderson localization, the study of polaron systems and the non-equilibrium statistical mechanics of coupled anharmonic oscillators. The conference will provide a venue for the dissemination or recent results and methods in the area and will foster further advances in these important topics. A strong component of this conference is educational and aimed at disseminating recent advances in classical, quantum and statistical mechanics. Emphasis will be placed on encouraging interactions between senior and junior researchers. Special efforts will be made to invite and support graduate students, postdocs, as well as mathematicians from underrepresented groups. The study of the evolution of systems with infinite number of degrees of freedom is ubiquitous in modern science. In the situation pertaining to classical mechanics, a typical example is that of the evolution of a fluid where a degree of freedom essentially corresponds to the velocity of the fluid at some point in space. Since there are infinitely many such points one is looking at a complex system with infinitely many degrees of freedom in interaction. These give rise to nonlinear partial differential equations which feature in a huge number of applications such as the models used for weather prediction. In the quantum case, examples of such systems are the polaron systems which describe the motion of particles in an ionic crystal (structures similar to that of ordinary salt). Another example studied under the name of Anderson localization has to do with the motion of a quantum particle in interaction with a random medium. The latter is supposed to model, e.g., the impurities in a semiconductor. Finally, a third regime where systems with infinitely many degrees of freedom are the subject of very active study is that of statistical mechanics, in particular in the non equilibrium situation. An example of mathematical challenge in the area is to understand the conduction of heat or electricity, not in an ad hoc phenomenological description, but rather through a derivation from first principles: the basic laws of classical or quantum mechanics at the microscopic level.