中科院数学与系统科学研究院

数学研究所

学术报告

几何分析研讨班

时  间：2022.07.06（星期三）

地  点：腾讯会议：112-551-522

n  上午9：00-10：00

报告人：宋翀 （厦门大学）

题  目：Finite-time singularities of 2d V-harmonic map flow

摘 要：The V-harmonic map is a natural generalization of the harmonic map, but lack of a variational structure in general. We find that when V is conformal, the evolution and blow-up of 2d V-harmonic map flow still share same properties with the ordinary harmonic map flow. In particular, the finite-time singularities must locate at zeroes of V when the blow-up rate is sufficiently slow.

n  上午10：00-11：00

报告人：郑恺 （同济大学）

题  目：Singular scalar curvature equations

摘 要：We will present recent progress on the singular scalar curvature equations. We will further present some, but not all, applications, including

1. the extension of Chen-Cheng’s resolution of the properness conjecture and the geodesic stability conjecture for cscK metric with singularities, 2. an answer to Ross-Thomas’s question on logarithmic semi-stability and 3. the existence/uniqueness of canonical metrics on singular varieties.

n  上午11：00-12：00

报告人：石亚龙 （南京大学）

题  目：Constant scalar curvature Ka ̈hler metrics on ramified Galois covers

摘 要：Let f:M→N be a finite ramified Galois cover between compact  Ka ̈hler manifolds. If N has a cscK metric, under suitable conditions, we shall prove the existence of cscK metrics on M. This generalizes previous works of Arezzo-Ghigi-Pirola and Li-Sun on Ka ̈hler-Einstein metrics. This is joint work with Claudio Arezzo and Alberto Della Vedova.