Geometry Seminar

Talk 1：李子鈺 YMSC

13:00 - 14:15

Oka theory in the homotopy-theoretic viewpoint

Gromov's 1989 paper is the foundation work of Oka theory, in which he describes many of his insightful ideas. In this paper, Larusson saw the shadow of Quillen's first axiom for a model category, which inspired him use homotopical algebra to study lifting and extension properties of holomorphic maps, such as those given by the Oka Principle. In this talk, we will introduce this abstract process of Oka theory.

Talk 2：周胜铉 Peking University

14:30 - 15:45

Bergman kernels on degenerations

In this talk, we consider the fiberwise Bergman kernel for a flat family of polarized varieties over a Riemann surface. We will explain the continuity of the fiberwise Bergman kernel and give a result on uniform convergence for the Fubini-Study currents. This is a joint work with Linsheng Wang.

Talk 3：叶亚楠 Peking University

16:00 - 17:15

Bismut Einstein metrics on compact complex manifolds

We observe that, for a Bismut Einstein metric, the (2,0)-part of Bismut Ricci form is an eigenvector of the Chern Laplacian. With the help of this observation, we prove that a Bismut Einstein metric with non-zero Einstein constant is Kähler Einstein. Additionally, for Bismut Einstein metrics with zero Einstein constant, we prove that they are actually Bismut Ricci flat.