Time：9:00-10:30, Friday, December 26 2025
Tencent Meeting：898 3182 7279
Password: 541944
Host：Jintian Zhu, ITS
Speaker：Zehao Sha, USTC
Title：The $2$-systole on compact Kähler surfaces with positive scalar curvature
Abstract：In this talk, I will introduce a systolic inequalities on compact Kähler surfaces with positive scalar curvature (PSC). For a compact PSC Kähler surface $(X,\omega)$, I will explain how to prove the sharp inequality $\min_X S(\omega) sys_2(\omega) \leq 12\pi$ with equality if $X\simeq P^2$ endowed with $\omega$ the Fubini-Study metric. Using the classification of PSC Kähler surfaces by their minimal models, we then determine the optimal constant in each case and describe the corresponding rigid models. If time permits, I will introduce an independent analytic argument on non-rational PSC Kähler surfaces, adapting Stern’s level set method to the Kähler setting.
