报告内容简介：
In this talk, we introduce a metric on the space of filtrations on a Noetherian local ring, which is the local counterpart of the Darvas metric on the space of K?hler potentials on a K?hler manifold and that on the space of norms on the section ring of a polarized variety introduced by Boucksom-Jonsson. This metric justifies the prior notion of geodesics between filtrations, in the sense that it is a continuous curve with minimal length. We describe the space concretely in the toric setting. If time permits, we will also discuss several applications and potential interactions with commutative algebra, birational geometry, non-archimedean analysis and K-stability in charateristic p. Partially based on joint work with Harold Blum and Yuchen Liu.

报告人简介：
本科毕业于北京大学，普林斯顿大学博士。主要从事代数几何的理论研究，在双有理几何和K稳定性领域得到了一系列结果，相关成果发表于Amer. J. Math.、J. Algebraic Geom.等著名期刊。