图 书 馆
相切和判别式Tangency and Discriminants |
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| 课程网址: | http://videolectures.net/FPSAC2019_di_rocco_tangency_and_discrimi... |
| 主讲教师: | Sandra Di Rocco |
| 开课单位: | 皇家理工学院 |
| 开课时间: | 2019-07-19 |
| 课程语种: | 英语 |
| 中文简介: |  具有指定单项式的多项式的判别式是当相应多项式有多个根时系数消失的不可约多项式。它是多项式数值研究中的重要工具，并描述了相关代数簇的丰富相切几何。我将回忆这种相互作用并介绍多项式系统的判别式（混合判别式）的概念。然后，我将展示导致迭代判别式概念的广义 Schäfli 方法如何简化混合判别式的分析。演讲将主要介绍该主题。最新结果基于与艾丽西亚·迪肯斯坦 (Alicia Dickenstein) 和拉尔夫·莫里森 (Ralph Morrison) 的合作。 |
| 课程简介: | The discriminant of a polynomial with prescribed monomials is an irreducible polynomial in the coefficients vanishing when the corresponding polynomial has multiple roots. It is an important tool in numerical studies of polynomials and describes a rich geometry of tangency of an associated algebraic variety. I will recall this interplay and introduce the notion of discriminant for a system of polynomials (the mixed discriminant). I will then show how a generalised Schäfli method leading to the notion of iterated discriminant can simplify the analysis of mixed discriminants. The talk will mostly be introductory to the subject. The latest results are based on joint work with Alicia Dickenstein and Ralph Morrison. |
| 关 键 词: | 单项式; 多项式 |
| 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: | 54 |