图 书 馆
图的组合迭代积分和单能托雷利定理Combinatorial iterated integrals and the unipotent Torelli theorem for graphs |
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| 课程网址: | http://videolectures.net/FPSAC2019_katz_iterated_integrals/ |
| 主讲教师: | Eric Katz |
| 开课单位: | 滑铁卢大学 |
| 开课时间: | 2019-07-19 |
| 课程语种: | 英语 |
| 中文简介: |  经典的托雷利定理说黎曼曲面可以从它的雅可比矩阵中恢复出来，雅可比矩阵是一个主要极化的阿贝尔变体。由于 Artamkin 和 Caporaso-Viviani，图有一个类似的定理，即可以从其循环空间中恢复图的 2 同构类，并配备其循环配对。我们会问，当考虑温和的非阿贝尔数据时会发生什么，如由于 Hain 和 Pulte 的黎曼曲面的单能 Torelli 定理。这导致我们在图上引入迭代积分的类似物，并将它们编码在特定结构中。事实证明，这种结构可以恢复指向同构的无桥图。我们讨论了这个结果的一些应用以及与霍奇理论、热带几何学和数论的联系。这是与 Raymond Cheng 的合作。 |
| 课程简介: | The classical Torelli theorem says that a Riemann surface can be recovered from its Jacobian, which is a principally polarized Abelian variety. There is an analogous theorem for graphs, due to Artamkin and Caporaso–Viviani that the 2-isomorphism class of a graph can be recovered from its cycle space, equipped with its cycle pairing. We ask what happens when one considers mildly non-abelian data as in the unipotent Torelli theorem for Riemann surfaces due to Hain and Pulte. This leads us to introducing the analogue of iterated integrals on graphs and encoding them in a particular structure. This structure turns out to recover pointed bridgeless graphs up to isomorphism. We discuss some of the application of this result and connections to Hodge theory, tropical geometry, and number theory. This is joint work with Raymond Cheng. |
| 关 键 词: | 黎曼曲面; 雅可比矩阵; 无桥图 |
| 课程来源: | 视频讲座网 |
| 数据采集: | 2021-06-04：yumf |
| 最后编审: | 2021-06-04：yumf |
| 阅读次数: | 37 |