77779193永利官网计算数学系列会议——符号计算研讨会

会议形式：网络会议

会议日期：2020年11月28日上午8:40-11:20

加入方式：腾讯会议ID： 607 107 598 密码：1128

会议日程：

报告题目: Chordal Graphs in Triangular Decomposition in Top-Down Style

报告人：牟晨琪 副教授

（北京航空航天大学数学科学学院）

摘要：In this talk, I will present some underlying connections between chordal graphs from graph theory and triangular decomposition in top-down style from symbolic computation. Viewing triangular decomposition in top-down style as polynomial generalization of Gaussian elimination, we show that all the polynomial sets, including all the computed triangular sets, appearing in several typical algorithms for triangular decomposition in top-down style have associated graphs which are subgraphs of the chordal graph of the input polynomial set. These theoretical results can be interpreted as “triangular decomposition in top-down style preserves chordality” and are used to design sparse triangular decomposition for polynomial sets which are sparse with respect to their variables. Extension to ordinary differential triangular decomposition will also be discussed, if time permits.

This talk is based on the joint work with Yang Bai and Jiahua Lai.

报告题目: Mechanical Proofs of Combinatorial Identities

报告人：陈绍示 副研究员

(中国科学院数学与系统科学研究院, 数学机械化重点实验室)

摘要: This talk will give a glimpse into the so-called Wilf-Zeilberger theory. We will show when and how a given combinatorial identity can be proved automatically. Motivated by Nicole’s theorem and criteria on the summability of rational functions, we are also able to prove identities

involving hypergeometric or even non-holonomic terms.

This is a joint work with Rong-hua Wang.

报告题目: 基于代数方法的Keccak(SHA-3)算法原像攻击

报告人：孙瑶 研究员

（中国科学院信息工程研究所）

摘要：继MD5和SHA-1算法相继被发现严重安全隐患后，美国标准技术研究院(NIST)于2008年举办了SHA-3竞赛，公开向全世界征集新一代hash标准，最后Keccak算法于2012年在竞赛中胜出，并在2015年被正式确认为第三代hash函数标准。目前Keccak（SHA-3）算法已经广泛的应用于社会生活的各个领域。在本次报告中，我们提出了一种全新的“交叉线性”代数结构，这是一种特殊的非线性代数结构。我们利用这个结构对Keccak算法进行了原像攻击，并攻破了一个提出6年的Keccak算法国际公开挑战问题，这也是迄今为止最后一个被攻破的Keccak挑战问题。

报告题目: Unirational Differential Curves and Differential Rational Parametrizations

报告人：李伟 副研究员

（中科院数学与系统科学研究院）

摘要：In this talk, we present our recent work on unirational differential curves and the corresponding differential rational parametrizations. We first investigate the basic properties of proper differential rational parametrizations for unirational differential curves. Then we show the implicitization of proper linear differential rational parametric equations could be solved by means of differential resultants. Furthermore, for linear differential curves, we give a criterion to decide whether an implicitly given linear differential curve is unirational and compute a proper differential rational parametrization in the affirmative case. This is joint work with Lei Fu.