摘要:

Singularities of differential operators or recurrence operators are points at which the numerical computation of solutions is cumbersome. In some cases, this is unavoidable because there is a solution which has a strange behaviour (e.g. a pole) at this point. But sometimes a singularity of a differential operator is only a "false alarm" and does not really correspond to a singularity of a solution. Such singularities are called apparent. Desingularization algorithms eliminate apparent singularities from a given operator. For differential operators such algorithms were already known in the 19th century, and for recurrence operators they were worked out by Abramov and van Hoeij in the 1990s. In the talk we will explain the ideas behind these techniques and then present a recent observation made in joint work with Shaoshi Chen and Michael Singer that leads to a more elegant and more general desingularization algorithm.

报告人简介：

Manuel Kauers 博士是奥地利林茨大学符号计算研究所副教授，博士生导师。他的研究邻域是符号分析（积分与求和）及其在计数组合学中的应用。从2003年至今，他在其研究邻域里取得一系列高水平的成果，特别是分别于2009年和2011年利用符号计算方法成功解决了组合数学中两个重要猜想：Gessel's Lattice Path Conjecture 与George Andrews' and David Robbins' q-TSPP-Conjecture。 这两项结果均发表于国际顶级杂志《美国国家科学院院刊》。Kauers 博士现为国际符号与代数计算会议(ISSAC)的Steering Committee 3名成员之一， 国际应用数学杂志 Adv. in App. Math. 编委之一。