勷勤数学•专家报告

题      目：Structure of critical points of multiple Green functions on flat torus and applications

报  告  人：陈志杰 教授  (邀请人：钟学秀)

                                              清华大学

时      间： 11月8日  12：00-13:00

地     点：数科院西楼二楼会议室

报告人简介:

          陈志杰，清华大学数学系和数学中心长聘教授，近年来主要研究椭圆偏微分方程与可积系统、数论等其他领域的交叉应用。在平均场方程、Toda系统、Lame方程、Eisenstein级数等课题取得了系列重要的成果，部分论文发表在Adv.Math, Amer.J.Math, ARMA, Comm.Math.Phys, Crelle, J.Differ.Geom等权威期刊上。

摘      要：

        In this talk, I will introduce our recent progress on the study of the multiple Green function G_n on flat torus. Lin and Wang (Ann. Math 2010) proved that G_1 has exactly three trivial critical points and at most one pair of nontrivial critical points. For general n, Chai, Lin ang Wang (Camb. J. Math. 2015) proved that G_n has at most 2n+1 trivial critical points, but how many nontrivial critical points might exist remained completely open there. Now we can prove that G_n has at most n pairs of nontrivial critical points, and this upper bound is optimal at least for n=2,3. Applications to the curvature equation will be given. In particular, we show that the kernel of the linearized operator is one-dimensional for any solution of the curvature equation.

          欢迎老师、同学们参加、交流！