报告题目: Convexity of multiplicities of filtrations on local rings
报告人：戚鲁(普林斯顿大学)
时间： 2023-3-30 9:00-10:00
地点: 腾讯会议809-386-427
邀请人：孙鹏
报告摘要: In this talk, I will discuss some convexity properties of multiplicities of filtrations on a local ring. In particular, the multiplicity function is convex along geodesics. As a major application, we get a new proof of a theorem due to Xu and Zhuang on the uniqueness of normalized volume minimizers. In order to characterize strict convexity, we introduce the notion of saturation of a filtration, which turns out to be useful in other settings. For example, it allows us to generalize a theorem of Rees on multiplicities of ideals and characterize when the Minkowski inequality for filtrations is an equality. This talk is based on joint work with Harold Blum and Yuchen Liu.
报告人简介：戚鲁，本科毕业于北京大学，普林斯顿大学博士在读,导师为许晨阳教授。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。
