图 书 馆
图的组合迭代积分和单能Torelli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，可以从其Jacobian（主要是极化的Abelian变种）中恢复Riemann表面。由于有Artamkin和Caporaso-Viviani，图有一个类似的定理，图的2个同构类可以从其循环空间（配有循环配对）中恢复。我们问，当人们考虑到温和的非阿贝尔数据时（如因海因和普尔特而引起的黎曼曲面的单能Torelli定理），会发生什么。这导致我们在图上引入迭代积分的类似物并将其编码为特定的结构。事实证明，这种结构可恢复有尖的无桥图，直至同构。我们讨论了该结果的一些应用以及与霍奇理论，热带几何和数论的联系。这是与郑浩文的共同作品。 |
| 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: | 托雷利定理说; 循环空间; 非阿贝尔数据 |
| 课程来源: | 视频讲座网 |
| 数据采集: | 2020-11-29：cjy |
| 最后编审: | 2020-11-29：cjy |
| 阅读次数: | 39 |