Geometry Seminar

Abstract：

13:00 - 14:15 王淋生

Title:

A new example of Fano manifold with Kähler-Ricci soliton

Abstract: In this talk, I will intr

oduce an effective method to show the existence of the Kähler-Ricci soliton on a given Fano manifold. As an application, we show that any Fano threefold X in the family No.2.28 of Mukai-Mori's list (that is, CP^3 with a smooth plane cubic curve C blowup) admits Kähler-Ricci soliton. Furthermore, we show that the weighted K-stability of the Fano manifolds X is equivalent to the GIT-stability of the plane cubic curves C. This is a joint work with Minghao Miao.

14:30 - 15:45 河井公大朗

Title:

Mirror of minimal submanifolds and a monotonicity formula

Abstract: For Hermitian connections on a Hermitian complex line bundle over a Riemannian manifold, we can define the "volume", which can be considered to be the "mirror" of the standard volume for submanifolds. We call the critical points minimal connections. They can be considered as "mirrors" of minimal submanifolds and analogous to Yang-Mills connections.

In this talk, I will introduce some properties of minimal connections and then state a monotonicity formula. As a corollary, we obtain the vanishing theorem for minimal connections in the odd-dimensional case.

16:00 - 17:15 谢松晏

Title:

Entire curves generating all shapes of Nevanlinna currents

Abstract: Nevanlinna currents were introduced by McQuillan to capture asymptotic behaviors of entire curves. In this talk, we will show that from some single entire curve we can obtain quite distinct Nevanlinna currents.