论文标题
表面和拓扑字符串的枚举几何形状
Enumerative geometry of surfaces and topological strings
论文作者
论文摘要
这项调查涵盖了关于looijenga对的几何和物理学的最新发展，即$（x，d）$与$ x $ a a $ x $ a复杂的代数表面和$ d $ a the the the It中的单数反典型分裂。我将描述一个令人惊讶的通讯网络，将与$（x，d）$相关的几个先验遥远的枚举不变式链接在一起，包括这对夫妇的log gromov - gromov，gromov- gromov- gromov- witten的不变式，是相关的更高尺寸的calabi calabi calabi and open gromovs intery noven noven intery and novery intery and toragrane int tor coatians intriant and toragrane int tor coatians，唐纳森（Donaldson） - 一类对称箭的托马斯理论，以及某些开放和封闭的BPS型不变性。我还将讨论如何有效地使用这些对应关系来为所有这些不变的计算提供完整的封闭式解决方案。
This survey covers recent developments on the geometry and physics of Looijenga pairs, namely pairs $(X,D)$ with $X$ a complex algebraic surface and $D$ a singular anticanonical divisor in it. I will describe a surprising web of correspondences linking together several a priori distant classes of enumerative invariants associated to $(X,D)$, including the log Gromov--Witten invariants of the pair, the Gromov--Witten invariants of an associated higher dimensional Calabi--Yau variety, the open Gromov--Witten invariants of certain special Lagrangians in toric Calabi--Yau threefolds, the Donaldson--Thomas theory of a class of symmetric quivers, and certain open and closed BPS-type invariants. I will also discuss how these correspondences can be effectively used to provide a complete closed-form solution to the calculation of all these invariants.
