论文标题
扩展的热带顶点组
The extended tropical vertex group
论文作者
论文摘要
在这篇论文中，我们研究了基于Chan-Conan Leung-Ma的最新作品，研究了散射图和全体形态对的变形之间的关系。新功能是扩展的热带顶点组，其中定义了散射图。此外，扩展的热带顶点还提供了有趣的应用：一方面，我们可以对耦合的墙壁交叉公式进行几何解释，以$ 2D $ - $ 4D $系统，以前是Gaiotto-Moore-Moore-Neitzke。另一方面，格罗莫夫（Gromov） - 相对于其边界除数的不变型出现在换向器公式中，以及由于毛 - 帕达里列尼（Pandharipande-siebert）而引起的某些绝对不变剂，这表明在几何学和数学物理学方面可能与开放/封闭的理论有可能的联系。
In this thesis we study the relation between scattering diagrams and deformations of holomorphic pairs, building on a recent work of Chan--Conan Leung--Ma. The new feature is the extended tropical vertex group where the scattering diagrams are defined. In addition, the extended tropical vertex provides interesting applications: on one hand we get a geometric interpretation of the wall-crossing formulas for coupled $2d$-$4d$ systems, previously introduced by Gaiotto--Moore--Neitzke. On the other hand, Gromov--Witten invariants of toric surfaces relative to their boundary divisor appear in the commutator formulas, along with certain absolute invariants due to Gross--Pandharipande--Siebert, which suggests a possible connection to open/closed theories in geometry and mathematical physics.
