报告人：Shaoshi Chen（Academy of Mathematics and Systems Science, Chinese Academy of Sciences）
时间：2018-12-18 14:30-15:30
地点：Room 1570, Sciences Building No. 1
Abstract: D-finite functions are solutions of systems of linear partial differential equations with polynomial
coefficients of special type. This class of functions has been systematically investigated by R. Stanley in his
book Enumerative Combinatorics (Volume II) as basic generating functions in combinatorics. In this talk, we
will present some results related to three aspects of D-finite functions. In the algorithmic aspect, we will
present some basic symbolic algorithms for manipulating D-finite functions. In the analytic aspect, we will
study the apparent singularities of D-finite functions and the corresponding desingularization algorithms.
In the arithmetic aspect, we prove that a multivariate D-finite power series with coefficients from a finite set
is rational. This generalizes a rationality theorem of van der Poorten and Shparlinski in 1996. As an application,
we will show how these results can be used to study the nonnegative integer points on algebraic varieties.
This talk is based on my joint papers with Jason P. Bell, Manuel Kauers, Ziming Li, Michael F. Singer and Yi Zhang.
报告人简介：陈绍示，主要研究符号计算，计算微分代数与代数组合学(Wilf-Zeilberger 方法,形式幂级数理论等)，现为
中国科学院数学与系统科学研究院副研究员, 博士生导师。2011年中国科学院与法国巴黎综合理工学校联合培养博士毕
业，曾先后在奥地利 Linz 大学符号计算研究所、美国北卡罗来纳州立大学、加拿大菲尔兹数学研究所与滑铁卢符号计
算研究组从事博士后工作。2013年回国到中科院数学与系统科学研究院系统所工作，2017年晋升为副研究员。先后主
持国家自然科学青年基金，教育部留学回国人员科研启动基金，与国家自然科学面上基金. 在符号计算领域权威会议
ISSAC 录用论文12篇，以及 Journal of Symbolic Computation，Journal of Algebra,和 Journal of Combinatorial
theory, Series A 等期刊发表论文 10 余篇。获得国际符号与代数计算年会“ISSAC2014 杰出海报奖”和中国科学院数学
与系统科学研究院“2014 年突出科研成果奖”。入选中国科学院第七届“陈景润未来之星”人才计划和中国科学院2018年度青年创新促进会会员。
