主题：A generalization of Michael-Simon-Sobolev inequality and higher eigenvalues estimate

时间：2023年5月24号 10:00-11:30

地点：腾讯会议：375-202-671

主持人：种田 副教授

报告人简介：

　　林和子，福建师范大学数学与统计学院副教授。主要研究方向为：子流形几何，几何分析，等周不等式等。在J. Geom. Anal., Quart. J. Math.,Tohoku Math. J.等国内外数学杂志发表SCI论文22篇。

讲座简介：

　　In this talk, we first show a Michael-Simon Sobolev inequality in a more general ambient space which supports a special distance type function. Based on this Michael-Simon Sobolev inequality, we obtain some estimates on the higher eigenvalues of submanifolds in terms of the volume of submanifolds. Finally, we give some upper bounds of the number of eigenvalues for Schrodinger operator on submanifolds. This is a joint work with Yuxin Dong and Lingen Lu.

主题：Defocusing NLS equation with a nonzero background: Painleve asymptotics in two transition regions

时间：2023年5月16号 15:00-16:30

地点：腾讯会议: 928638033

主持人：罗琳 教授

报告人简介：

　　范恩贵，复旦大学数学科学学院教授、博士生导师。主要研究方向是可积系统、Riemann-Hilbert问题、正交多项式和随机矩阵理论。主持国家自然科学基金、上海曙光计划等多项研究课题。在《Advance in Mathematics》、《SIAM Journal of Mathematical Analysis》、《Journal Differential Equations》等国际重要期刊发表论文100余篇，被SCI刊源他引3000余次。获教育部自然科学二等奖、上海市自然科学二等奖、复旦大学谷超豪数学奖等荣誉。

讲座简介：

      We address the Painleve asymptotics in the transition region of the solution to the Cauchy problem for the defocusing nonlinear Schrodinger (NLS) equation with finite density initial data. The key to prove this result is the formulation and analysis of a Riemann-Hilbert problem associated with the Cauchy problem on the basis of direct and inverse scattering transform of the Lax pair of the defocusing NLS equation. Further with the dbar-generation of the nonlinear steepest descent method and double scaling limit technique, in two transition regions, we find that the leading order approximation to the solution of the defocusing NLS equation can be expressed in terms of the solution of the Painleve II equation.

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