讲座题目： Some new progress on Sharp Trudinger-Moser inequality and bubbling analysis for its positive critical point.

主办单位：三峡数学研究中心/理学院

报告专家：陈露 副研究员（北京理工大学）

报告时间：2021年11月12日（周五）下午（14:30—17: 30）

报告地点：腾讯会议（ID： 236 577 271）

专家简介：陈露，北京理工大学数学与统计学院副研究员。2018年博士毕业于北京师范大学，2019年在意大利比萨高师跟从国际著名的几何和变分领域的大师Malchiodi做访问学者。长期致力于研究Trudinger Moser不等式及其在几何分析与偏微分方程中的应用。相关结果发表在Adv. Math, Trans. AMS, J. Funct. Anal, Calc.Var& PDE，JGA, 中国科学等国际知名SCI学术期刊。

报告摘要：Trudinger-Moser inequalities as the border line case of Sobolev inequalities have important applications in the fields of geometric analysis and PDEs. In this talk, I will give a survey about the history of Trudinger-Moser inequality and its important role in prescribing curvature problem and Schrodinger-equation with the critical exponential growth.  Then I will present some new progress on sharp Trudinger-Moser inequalities including Trace Trudinger-Moser inequalities, Trudinger-Moser involving degenerate potential and affine Trudinger-Moser inequalities, etc. Finally, quantization theory for the critical point of Trudinger-Moser functional in compact and non-compact manifolds will also be discussed in this talk.