基础数学系学术报告

--北航微分几何讨论班（2021春第9讲）

题目：Domination results in n-Fuchsian fibers

报告人：戴 嵩 副教授（天津大学）

时间：2021年5月14日 9:30-10:30

地点：沙河校区E404

摘要：We start this talk with some basic linear algebras. Consider m(A)=[A,A*] on sl(n,C). Ness studied the (normalized) square of norm |m|^2 and showed some nice properties of |m|^2 which characterize the unitary orbits inside the nilpotent orbits of sl(n,C). We generalize Ness’ results to general orbits by modifying |m|^2, motivated by the curvature formula of the symmetric spaces. As applications, we show some domination results in n-Fuchsian fibers in the Hitchin fibration of the moduli space of Higgs bundles over a Riemann surface. And we also show some existence and uniqueness results of equivariant minimal surfaces in certain product spaces, which generalize a theorem of Schoen.

报告人简介：戴嵩，现为天津大学应用数学中心副教授，2010年本科毕业于南开大学，2015年博士毕业于北京大学，师从田刚院士。主要研究方向为微分几何，已经在JDG., Math.Ann.等国际著名数学期刊上发表多篇论文。

邀请人：张世金、沈良明