台湾中央研究院叶永南研究员学术报告

时间:2019-03-04浏览:13设置

报告人:叶永南 教授(Yeong-Nan Yeh,台湾中央研究院)


时    间:201935日上午1030—1130


地    点:数计学院21427


题    目:Asymptotic normality criteria of coefficients of a polynomial and their applications in combinatorics


摘    要:The asymptotic distribution theory for coefficients of a polynomial is an active topic in asymptotic analysis. In 1967, Harper proposed a criterion to measure the asymptotic normality of a series of numbers, when he researched the asymptotic behavior of Stirling numbers of the second kind. In this paper, we aim to develop some further asymptotic normality criteria of coefficients of a polynomial with all real roots or purely imaginary roots (including 0). These new asymptotic normality criteria turn out to be very efficient and have abundant applications in combinatorics, mainly including the coefficients of a series of characteristic polynomials of adjacency matrix, Laplacian matrix, signless Laplacian matrix, skew-adjacency matrix, chromatic polynomial, and some graph numbers, such as matching numbers, independence numbers, clique numbers. Among which, we generalize and verify some conjectures about asymptotic normality in combinatorics, e.g., the matching numbers proposed by Godsil and Kahn , the (signless) Laplacian coefficients claimed by Wang et al.



个人简介:叶永南,台湾中研院数学所研究员, 1985年在美国纽约州立大学获博士学位。1987年返台担任中央研究院数学所副研究员。19911月晋升为研究员迄今。曾任加拿大魁北克大学资讯与数学系研究学者,麻省理工学院数学系、柏克莱加州大学统计系和澳洲Monash大学经济系访问学者。曾任台北数学推动中心主任, 中研院数学所副所长。学术研究除数学外, 还涉及物理、化学、统计、经济等多个领域。多次获得台湾杰出研究奖, 杰出研究计划奖。组合论国际顶级杂志JCTA曾出版专门文章介绍Yeh-species,这个由叶永南研究员名字命名的领域, 现在这一方向的研究仍然在不断深入。





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