2006年国际数学家大会一小时报告人
Richard P. Stanley教授

报告 I：曹锡华数学论坛系列讲座
Alternating permutations (交错排列)

时 间: 2009年1月6日（星期二）15:00—16:00
地 点：闵行校区数学楼102报告厅

摘 要：A permutation $a_1,a_2, dots,a_n$ of $1, 2, dots, n$ is called emph{alternating} if $a_1>a_2a_4 $$ sum_{ngeq 0}E_nfrac{x^n}{n!} = sec x+tan x, $$ found by D'esir'e Andr'e in 1879. We will discuss this result and how it leads to the subject of ``combinatorial trigonometry.'' We will then survey some further aspects of alternating permutations, including some other objects that are counted by $E_n$, a connection with the $cd$-index of the symmetric group, and the use of the representation theory of the symmetric group to count certain classes of alternating permutations.


报告II：A survey of plane tilings
(平面拼图中的数学问题)
时 间: 1月8日（星期四）15:20—16:20
地 点：闵行校区第三教学楼109报告厅

摘 要：Let R be a region in the plane, and let C be a collection of plane figures (tiles). A tiling of R by C is a filling of R with copies of the pieces of C without overlap or gaps. A well-known example is the Chinese puzzle tangram (七巧板), where the set of tiles is fixed but many different regions R are considered. We will survey the basic aspects of plane tilings, focusing on tilings of bounded regions with finitely many tiles. We will consider such questions as the following. Is there a tiling? If so, how many? If we can't say exactly how many tilings there are, is there a good approximation? Is a tiling easy to find? Is it easy to convince someone that a tiling doesn't exist? What does a “typical” tiling look like? How are different tilings related? These questions involve interesting aspects of combinatorics, computer science, logic, algebra, geometry and analysis. The talk should be accessible to an undergraduate math major.

报告人简介
Richard P. Stanley教授1966年毕业于加州理工学院，1971年获得哈佛大学博士学位，导师是组合数学大师G. C. Rota。1971年至1973年在Berkeley做研究，1973年起在美国麻省理工学院任教，现在是应用数学教授，美国艺术与科学院院士，美国科学院院士。
1975年Stanley教授荣获工业与应用数学学会SIAM授予的应用组合学的Pólya奖。2001年获得Steele数学论述奖，此奖主要授予他的著作《组合计数》（Enumerative Combinatorics），该著作共2卷，分别于1986年和1999年出版，被普遍认为是近年来组合领域的权威著作。2003年获得由瑞典皇家科学院颁发的Schock奖。 2005年8月应邀在西班牙举行的国际数学家大会上做一小时报告。