题目：Blowup solutions and vanishing estimates for singular Liouville equations

时间：2022年3月17日上午09:00-11:00

形式：腾讯会议 会议号：995-350-999

Abstract:The singular Liouville equation is a class of second order elliptic partial differential equations defined in two dimensional spaces:$$\Delta u+ H(x)e^{u}=4\pi \gamma \delta_0 $$, where $H$ is a positive function, $\gamma>-1$ is a constant and $\delta_0$ stands for a singular source placed at the origin. This deceptively simply looking equation has a rich background in geometry, topology and Physics. In particular it interprets the Nirenberg problem in conformal geometry and is the reduction of Toda systems in Lie Algebra, Algebraic Geometry and Gauge Theory. Even if we only focus on the analytical aspects of this equation, it has wonderful and surprising features that attract generations of top mathematicians. The structure of solutions is particular intriguing when $\gamma$ is a positive integer. In this talk I will report recent joint works with Juncheng Wei that give a satisfactory answer to important issues to this equation. I will report the most recent results, new insights and the consequences of these results.

报告人简介：张雷教授，2001年毕业于Rutgers（罗格斯）大学并获博士学位，现为佛罗里达大学教授，博士生导师。主要研究方向为非线性偏微分方程，几何分析。在Comm. Pure Appl. Math.，Comm. Math. Phys.，J. Euro. Math. Soc.，Adv. Math.，Math. Ann.，Proc. Lond. Math. Soc.，Tran. Amer. Math. Soc.，J. Funct. Anal.等国际顶级数学期刊上发表学术论文50余篇，主持美国国家自然科学基金多项。