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HMS范畴对称性与超几何系统HMS categorical symmetries and hypergeometric systems |
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| 课程网址: | https://videolectures.net/8ecm2021_spenko_hms_categorical/ |
| 主讲教师: | Špela Špenko |
| 开课单位: | 8ECM会议 |
| 开课时间: | 2021-07-06 |
| 课程语种: | 英语 |
| 中文简介: |  |
| 课程简介: | Hilbert’s 21st problem asks about the existence of Fuchsian linear differential equations with a prescribed ”monodromy representation” of the fundamental group. The first (slightly erroneous) solution was proposed by a Slovenian mathematician Plemelj. A suitably adapted version of this problem was solved, depending on the context, by Deligne, Mebkhout, Kashiwara-Kawai, Beilinson-Bernstein, ... The solution is now known as the Riemann-Hilbert correspondence. Homological mirror symmetry predicts the existence of an action of the fundamental group of the ”stringy K¨ahler moduli space” (SKMS) on the derived category of an algebraic variety. This prediction was established by Halpern-Leistner and Sam for certain toric varieties. The decategorification of the action found by HLS yields a representation of the fundamental group of the SKMS and in joint work with Michel Van den Bergh we show that it is given by the monodromy of an explicit hypergeometric system of differential equations. |
| 关 键 词: | HMS对称性; 超几何系统; 线性微分方程 |
| 课程来源: | 视频讲座网 |
| 数据采集: | 2024-05-29：liyq |
| 最后编审: | 2024-05-29：liyq |
| 阅读次数: | 1 |