Abstract:The systole of a closed Riemannian manifold is defined to be the length of a shortest noncontractible loop. Gromov's systolic inequality relates systole to volume, which is a curvature free inequality. Gromov proved that systolic inequality holds on closed essential manifolds. Gromov's further work indicates that systolic inequality is related to topological complicatedness of manifol...
AbstractAfter a review about Xiao's approach of Slope inequalities and its generalization to positive characteristic, a Miyaoka-Yau type inequality for a minimal smooth surface of general type is given as an application. This is based on some work with Professor Yi Gu, Hao Sun and Xiaotao Sun.SpeakerResearch Interestsmoduli of vector bundle