数学与统计学院 数学中心学术报告

时间：2011.12.26 (周一) 下午3:30~5:30

地点：数统大楼4楼 422 

报告一（3:30~4:30）

Title: Hadamard Matrices: An Introduction

Speaker: Prof. Qing Xiang (向青), University of Delaware

Abstract: A Hadamard matrix of order n is an n by n matrix H with entries +1 and -1 such that HH^T = nI, where I is the n by n identity matrix. The famous Hadamard matrix conjecture states that for every positive integer t, there exists a Hadamard matrix of order 4t. This conjecture remains open. The smallest multiple of 4 for which no Hadamard matrix has been constructed is currently 668. In this talk, we will review some basic constructions of Hadamard matrices, and survey some recent results.

讲座是介绍性的，也欢迎本科生参加。

报告二（4:30~5:30）

Title:  Classical Combinatorial Statistics Revisited: Descents of Permutations in a Ferrers Board

Speaker: 宋春伟，北京大学数学科学学院

Abstract: The field of combinatorial statistics has been extensively investigated by combinatorists since the classical treatment of MacMahon almost a century ago. Our talk starts with a brief introduction of this fascinating filed, then from there we focus on permutations restricted in a Ferrers board to study their descent polynomials and $q$-analogues in terms of the inversion statistic. Particularly, our results may be applied to permutations with bounded drop (or excedance) size, for which the descent polynomial was first studied by Chung et al while our method presents an alternative approach. The content here is largely based on a joint work of Catherine Yan and the speaker.

报告人简介：

1. 向青教授

Qing Xiang received the Ph.D. degree in mathematics from the Ohio State University, Columbus, Ohio, in 1995. From 1995 to 1997, he was a Bateman
Research Instructor in the Department of Mathematics of California Institute of Technology (Caltech). Since 1997, he has been with Department of
Mathematical Sciences of University of Delaware, where he was promoted to Professor of Mathematics in 2006.

Qing Xiang was awarded the Kirkman Medal of the Institute of Combinatorics and its Applications in 1999. Since 2006, Professor Xiang has been
an Editor-in-Chief of the Electronic Journal of Combinatorics. He is also on the editorial board of Science in China (Mathematics), Designs, Codes and
Cryptography and Journal of Combinatorial Designs.

2. 宋春伟教授

2004年毕业于美国宾大(University of Pennsylvania)，获博士学位，现为北京大学数学科学学院副教授、北京数学会副秘书长，从事组合数学与图论领域的研究。

为什么一定要把向开理老师的和向青、宋春伟老师讲座的时间安排到有重叠呢？