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Local and Global Aspects of D-finite Functions
发布时间:2018-04-26     点击次数:
报告题目: Local and Global Aspects of D-finite Functions
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)
报告时间: 2018年05月09日 10:00--11:00
报告地点: 理学院东北楼四楼报告厅(404)
报告摘要:

 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 the local and global studies of D-finite functions. Singularity analysis explores the local behavior of analytic functions. In the local aspect, we will study the apparent singularities of D-finite functions  and the corresponding desingularization algorithms. In the global 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 this result can be used to study the nonnegative integer points on algebraic varieties. This talk is based on recent joint works with Jason P. Bell, Manuel Kauers, Ziming Li, Michael Singer and Yi Zhang.

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