Turán-type problem is a fundamental problem in extremal graph theory. The spectral Turán-type problem is a newly developed one in this field. Both of these two types of extremal problems attract more and more researchers’ attention. In this talk, we first introduce the background in this field. Then we present our new results related to some conjectures in (spectral) extremal problems, which also illustrate the internal relationship between Turán-type problems and spectral Turán-type problems. Finally, we propose some further research issues along this line. This is a joint work with Guantao Chen, Xingyu Lei, Yuantian Yu, et al.

李书超，华中师范大学数学与统计学学院教授，博士生导师。主要研究方向为极值图论与图谱理论, 研究成果相继在Journal of Graph Theory, European Journal of Combinatorics, Advances in Applied Mathematics、Electronic Journal of Combinatorics、Discrete Mathematics等多个重要国际学术期刊发表SCI论文100余篇；主持国家自然科学基金项目5项; 入选教育部``新世纪优秀人才支持计划"；主持完成的项目``图的几类不变量的研究"获湖北省自然科学奖三等奖；担任中国运筹学会图论组合分会常务理事、中国工业与应用数学学会图论组合及其应用专委会常务委员.