一、讲座主题

The Shannon Capacity of a Graph

二、时间

9月28日（周六）15:00

三、地点

中心校区知新楼B座924报告厅

四、主讲人

胡思煌

五、主讲人简介

胡思煌，山东大学网络空间安全学院教授、德国洪堡基金获得者。主要从事组合数学与信息交叉领域的研究，包括代数组合、编码与信息论、球与格填充等方向。已在《SIAM Journal on Discrete Mathematics》《IEEE Transactions on Information Theory》《Journal of Number Theory》等期刊发表多篇论文。2019年入选山东大学杰出中青年学者。

六、摘要

Shannon, known as“the father of information theory”, was the first to investigate the zero-error capacity of a discrete memoryless noisy channel. This quantity can be equivalently cast in terms of the confusion graph associated with the channel, thus is often referred to as the Shannon capacity of a graph. Despite the apparent simplicity of the problem, a general characterization of Shannon capacity remains elusive. In this talk, I will first present a new bound on the Shannon capacity via a variation on the linear program pertaining to the fractional independence number of the graph. Secondly, I will talk about the more general problem of characterizing the zero-error capacity of the discrete memoryless broadcast channel with two receivers. I will introduce a new notion of graph capacity that generalizes the Shannon capacity, and discuss its properties. This talk is based on joint work with Ofer Shayevitz (TAU) and Itzhak Tamo (TAU).

七、邀请人

王光辉 数学学院教授

八、主办

山东大学数学学院