应兰州大学萃英学院和数学与统计学院邀请，美国纽约市立大学William Sit教授来我校访问并作学术报告。

报告题目：Introduction to Computational Differential Algebra

报告时间：2015年8月4日（星期二）15:00

报告地点：观云楼802

报告人： William Sit教授

报告题目：Introduction to Computational Differential Algebra

报告时间：2015年8月5日（星期三）15:00

报告地点：观云楼801

报告人： William Sit教授

报告内容:

Under Ritt and his students, Kolchin, Levi, Raudenbush, Cohn and Rosenfeld, basic differential (and difference) algebra was developed from a constructive view point and the foundation they built has been advanced and extended to become applicable in symbolic computation.

In these talks, we begin with a review of the division algorithm and how it may be modified and used to perform reductions, first in polynomial rings, then in ordinary and finally in partial differential polynomial rings. The abstract notions of (partial) differential rings, fields, and differential polynomials will be covered and no prerequisite is necessary other than a first course in modern algebra. We will use examples to illustrate how differential polynomials may be ordered and manipulated algebraically using Euclidean-like division. The goal is to apply the reduction algorithms for ideal membership decisions, when possible, and to ``simplify'' a given system of algebraic differential equations by reducing the order, degree, and number of unknowns, or by breaking the system up into ``simpler'' systems. We will compare this with the analogous operations on algebraic systems. More formally, we will cover the concepts of term-ordering and ranking, partial reduction and reduction, autoreduced sets, Gr\"obner basis, characteristic sets and the basics of the Rosenfeld-Gr\"obner algorithm. The lectures will concentrate more on elementary concepts and advanced results will only be stated without proofs.

报告人简介:

William Sit教授师从微分代数大师Ellis Kolchin，于美国哥伦比亚大学获得博士学位。他长期从事微分伽罗华理论，罗巴代数和计算代数等多方面的研究，并参与研发和拓展Axiom和Mathematica等数学软件。他多年来主持微分代数的Kolchin讨论班，使其成为这一领域的主要国际论坛。他还组织了微分代数和计算代数领域的多次国际会议，包括各次Differential Algebra and Related Topics国际会议。今年此会议作为国际工程与应用数学家大会的分会场在北京召开。