报告人简介：

Quốc Anh Ngô，越南国立大学自然科学学院教授，现任数学、力学与信息学学院院长。博士毕业于新加坡国立大学，曾在法国图尔大学从事博士后研究，并在日本东京大学任项目研究员，主持多项越南国家基金项目。研究方向包括变分法、非线性偏微分方程、黎曼几何与几何分析及数学物理，在Adv. Math., Comm. Math. Phys., J. Math. Pures Appl., Math. Ann., IMRN, CVPDE, JFA, JDE等国际数学刊物上发表学术论文五十余篇。

报告简介：

This talk presents recent results on optimal Hardy-Littlewood-Sobolev (HLS) inequalities on product spaces. We discuss the main inequalities, sharp parameter conditions, and related extremal problems. We will also explore several open questions concerning the existence, classification, and uniqueness of extremal functions, as well as possible extensions to more general weighted kernels. Particular attention will be devoted to reversed HLS inequalities, including their validity on product spaces, sharp constants, admissible parameter ranges, and the existence or nonexistence of extremals. We will highlight several challenging problems in this direction, some of which can be traced back to questions posed by E. Lieb in 1983.