共形不变缩放极限（概述和问题集）
Conformally invariant scaling limits (an overview and a collection of problems)
摘要：
二维统计物理学的许多数学模型要么是已知的，要么是被证明具有共形不变性。多年来，物理学家提出了各种指数的预测来描述这些模型的行为。直到最近，这些预言中的一些才得到了数学证明。其中一个新的发展是发现了一个单参数的随机曲线族，称为随机Loewner演化或SLE。SLE曲线表现为在各种统计物理模型中出现的界面或路径的极限，因为在其上定义模型的网格趋于零。这篇文章的主要目的是列出一系列未决问题。一些未解决的问题表明物理知识的某些方面尚未被数学理解。其他问题是关于SLE曲线本身的性质的问题。在我们提出开放性问题之前，我们将对系统性红斑狼疮的定义进行解释，并简要介绍最近的研究结果。
英文摘要：
Many mathematical models of statistical physics in two dimensions are either known or conjectured to exhibit conformal invariance. Over the years, physicists proposed predictions of various exponents describing the behavior of these models. Only recently have some of these predictions become accessible to mathematical proof. One of the new developments is the discovery of a one-parameter family of random curves called Stochastic Loewner evolution or SLE. The SLE curves appear as limits of interfaces or paths occurring in a variety of statistical physics models as the mesh of the grid on which the model is defined tends to zero. The main purpose of this article is to list a collection of open problems. Some of the open problems indicate aspects of the physics knowledge that have not yet been understood mathematically. Other problems are questions about the nature of the SLE curves themselves. Before we present the open problems, the definition of SLE will be motivated and explained, and a brief sketch of recent results will be presented.
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