报告题目：Local mass concentration and a priori estimate for singular Toda systems of Rank 2.

报告人：张雷 教授

时间：2016-07-06

地点：数学与统计学院一楼报告厅

摘要：A Toda system is a nonlinear second order elliptic system with exponential nonlinearity. It is very commonly observed in physics and has many ties with algebraic geometry. From analytic viewpoints it is challenging since the solutions do not have symmetry, maximum principles cannot be applied and the structures of global solutions are incredibly complicated. In this joint work with Chang-shou Lin and Juncheng Wei, we use a unified approach to discuss all rank two singular Toda systems. First for local systems we prove that all weak limits of mass concentration belong to a very small finite set. Then for systems defined on compact Riemann surface we establish a priori estimate. Our approach is a combination of delicate blowup analysis and fundamental tools from algebraic geometry.

报告时间：7月6日上午10:30

报告人简介：

张雷，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。张雷教授的研究方向是：非线性偏微分方程。在Advances in Mathematics ，Comm. Pure Appl. Math.，J. Funct. Anal.，Comm. Math. Phys.，J. Diff. Equa.，Calc. Var. Partial Differential Equations，Proc. Amer. Math. Soc等国际著名期刊上发表学术论文40余篇，主持美国国家自然科学基金3项。2008年以来，应邀作学术报告48场。张雷教授是Advances in mathematics、Journal of differential equations、SIAM Journal on Mathematical Analysis、Proceedings of American Mathematical Society等24种国际期刊的审稿人。