Lectures on the Topological Recursion for Higgs Bundles and Quantum Curves
Lectures on the Topological Recursion for Higgs Bundles and Quantum Curves
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DOI：
10.1142/9789813229099_0003
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发表时间：
2015-09
期刊：
影响因子：
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通讯作者：
Olivia Dumitrescu;M. Mulase
中科院分区：
文献类型：
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作者：
Olivia Dumitrescu;M. Mulase
本文旨在介绍量子曲线的概念。主要目的是描述以下两个不同的主题之间的关系的新发现：一个是拓扑递归，它起源于随机矩阵理论，并已有效地应用于许多枚举几何问题;另一个是与希格斯束相关的希钦谱曲线的量子化。我们的重点是解释动机和例子。希钦谱曲线和计数问题之间的直接关系的具体例子。量子曲线的一般几何框架进行了讨论。
The paper aims at giving an introduction to the notion of quantum curves. The main purpose is to describe the new discovery of the relation between the following two disparate subjects: one is the topological recursion, that has its origin in random matrix theory and has been effectively applied to many enumerative geometry problems; and the other is the quantization of Hitchin spectral curves associated with Higgs bundles. Our emphasis is on explaining the motivation and examples. Concrete examples of the direct relation between Hitchin spectral curves and enumeration problems are given. A general geometric framework of quantum curves is also discussed.