题目: Graphs associated with matrices over finite fields and their endomorphisms
报告人: 李志光(Chi-Kwong Li) 教授, 美国威廉玛丽学院
摘要: Let be the set of matrices over a field F. Consider a graph G = ( , ) with as the vertex set such that two vertices A, B are adjacent if rank (A-B)=1. We study graph properties of G when F is a finite field. In particular, we show that G is a regular connected graph with diameter equal to min{m,n}; it is always Hamiltonian; it is Eulerian if and only if F has an odd number of elements.Furthermore,we determine the independence number,chromatic number and clique number of G. These results are used to characterize the graph endomorphisms of G, which extends Hua's fundamental theorem of geometry on .
Professor Chi-Kwong Li received his mathematics BA and PhD degrees from The University of Hong Kong. He is currently the Ferguson Professor of Mathematics at the College of William and Mary. Also, he is a 100 Talent Program Scholar of the Shanxi province at the Taiyuan University of Technology, an honorary professor of The University of Hong Kong, and an honorary professor of the Shanghai University. He has received many awards in research and teaching including the 2011 Fulbright Award, 2009 William and Mary Plumeri Award for Faculty Excellence, 2008 William and Mary Simon Teaching Prize, 2004 Virginia Outstanding Faculty Award. His research interest is on matrix, operator theory and their applications, and he has been focusing on quantum information science in recent years. He has published more than 270 research articles. He is the chief editor of two research journals, and is on the editorial boards of other two.
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