吉林大學計算數學系列會議——符号計算研讨會

會議形式：網絡會議

會議日期：2020年11月28日上午8:40-11:20

加入方式：騰訊會議ID： 607 107 598 密碼：1128

會議日程：

報告題目: Chordal Graphs in Triangular Decomposition in Top-Down Style

報告人：牟晨琪 副教授

（北京航空航天大學數學科學學院）

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.

報告題目: Mechanical Proofs of Combinatorial Identities

報告人：陳紹示 副研究員

(中國科學院數學與系統科學研究院, 數學機械化重點實驗室)

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.

報告題目: 基于代數方法的Keccak(SHA-3)算法原像攻擊

報告人：孫瑤 研究員

（中國科學院信息工程研究所）

摘要：繼MD5和SHA-1算法相繼被發現嚴重安全隐患後，美國标準技術研究院(NIST)于2008年舉辦了SHA-3競賽，公開向全世界征集新一代hash标準，最後Keccak算法于2012年在競賽中勝出，并在2015年被正式确認為第三代hash函數标準。目前Keccak（SHA-3）算法已經廣泛的應用于社會生活的各個領域。在本次報告中，我們提出了一種全新的“交叉線性”代數結構，這是一種特殊的非線性代數結構。我們利用這個結構對Keccak算法進行了原像攻擊，并攻破了一個提出6年的Keccak算法國際公開挑戰問題，這也是迄今為止最後一個被攻破的Keccak挑戰問題。

報告題目: Unirational Differential Curves and Differential Rational Parametrizations

報告人：李偉 副研究員

（中科院數學與系統科學研究院）

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.