Geometry Seminar

报告人 Speaker:刘亚雄(YMSC), 邓嘉龙(YMSC), 河井公大朗(BIMSA)
组织者 Organizer:FUTAKI AKITO
时间 Time:Sunday, 13:00 - 17:15 (PM), November 27,2022
地点 Venue:ONLINE: Zoom Meeting ID: 816 4977 5126 Passcode: Kahler


13:00 - 14:15 刘亚雄 Liu, Yaxiong (YMSC)

Title: Valuative stability of polarized varieties and applications.

Abstract: Recently, Dervan-Legendre considered the valuative criterion of polarized varieties. We will study the valuative stability and show that it is an open condition. We would like to study the valuative criterion for the Donaldson's J-equation. Motivated by the beta-invariant of Dervan-Legendre, we introduce a notion, the so-called valuative J-stability and prove that J-stability implies valuative J-stability. If time permits, we show the upper bound of the volume of K-semistable polarized toric varieties as an application of valuative stability.

14:30 - 15:45 邓嘉龙 Deng, Jialong (YMSC)

Title: The weighted scalar curvature

Abstract: Inspired by the importance  of the Bakry-Emery curvature on a weighted Riemannian manifold $(M^n, g, e^{f}Vol_g)$, we will introduce the weighted scalar curvature on it and then extend some classic results of the scalar curvature to the weighted version.  For example, we will generalize  Schoen-Yau's minimal hypersurface method, Gromov-Lawson's index theory approach and Seiberg-Witten invariants (in four dimensions) to  a weighted Riemannian manifold with positively  weighted scalar curvature.

16:00 - 17:15  河井公大朗 Kawai, Kotaro (BIMSA)

Title: Construction of nearly Kahler manifolds by Foscolo and Haskins

Abstract: A Riemannian 6-manifold is called nearly Kahler if its Riemannian cone has holonomy contained in G2. Only known examples were some homogeneous spaces for a long time, but Foscolo and Haskins constructed new cohomogeneity one nearly Kahler manifolds in 2017. I will explain an outline of the construction.