报告题目:Szego Limit Theorem and Mean Field Equations
主办单位:三峡数学研究中心/理学院
报告专家:胡烨耀博士(中南大学)
报告时间:2021年9月27日(周一)下午(14:30—16: 30)
报告地点:腾讯会议(ID:234 125 281)
专家简介:胡烨耀,2016年8月博士毕业于美国乔治华盛顿大学;2016年8月至2020年6月在UTSA担任博士后研究员;2020年9月起在中南大学任特聘副教授。主要从事非线性椭圆型偏微分方程的研究。近年来在《SIAM J. Math. Anal.》、《Int. Math. Res. Notices. IMRN》、《J. of Differential Equations》等国际权威期刊上发表论文多篇。
报告摘要:In this talk, we will first review the classical Lebedev-Milin inequality and Szego limit theorem on circle. PDE approach is adopted to establish infinitely many inequalities with vanishing higher order “moments” assumption through classifying the solutions of “Mean field equation” on circle. Then, higher dimensional analogues of Szego limit theorem of axially symmetric functions are introduced as byproducts of improved Beckner’s inequalities on spheres of even dimensions. This a joint work with Professor Changfeng Gui from UTSA and Dr. Weihong Xie from CSU.