讲座内容：

In1966,Kac asked a famaous question: “Can one hear theshape of a drum?”. This means, can two drums made ofthe same material, produce the same sound. An analogue of Kac’s question ingraph theory is “Can one hear the shape of a graph?”. This question originates from Chemistry in 1956. Mathematically, agraph G is said to be determined by its spectrum (DS for short), if any graphhaving the same spectrum as G is isomorphic to G.  “Which graphs aredetermined by their spectrum?” is a fundamentalquestion the spectral graph theory. It has attracted a lot of attention ofresearchers in recent years. Are almost all graphs DS, are almost all graphnon-DS, or is neiter true？In talk talk, I shall presentsome of our work towards answering the above question.