I: Regularity and V-filtration in dimension one II: On the theorems of Brionçon–Skoda and Varchenko
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：张鼎新（清华大学）
：2025-03-12 09:00
：海韵园实验楼S206 & 行政楼C610
报告人：张鼎新（清华大学）
时 间：2025年3月12日9:00 & 3月13日14:30
地 点：海韵园实验楼S206 & 行政楼C610
内容摘要:
I: We present the theory of regular holonomic D-modules over a one-dimensional base, with a focus on the V-filtration and vanishing cycle constructions. The study of the one-dimensional case provides insights that may extend to analogous constructions in higher dimensions.
II: Let f be a convergent power series in n+1 variables with an isolated critical point at 0. Consider the finite-dimensional C-algebra R = C{x₀,...,xₙ}/(∂f/∂x₀,...,∂f/∂xₙ). There exists an N such that fᴺ= 0 in R. The Brionçon–Skoda theorem states that we can take N = n+1. This remarkable result remained without an algebraic proof for many years. We will present Varchenko's interpretation of this theorem using D-modules and Hodge theory: if the Jordan blocks of the local monodromy operator acting on the Milnor fiber of f have sizes ≤ r, then fr= 0 in R.
个人简介：
张鼎新，清华大学助理教授。2017年纽约石溪大学博士毕业，2017-2019在哈佛大学和Brandeis大学从事博士后研究。研究方向为代数几何与算术几何, 特别是p-进和平展上同调理论以及在特征和方面的应用。相关研究成果发表在Compositio Math. Math. Ann.等国际著名期刊杂志上。
联系人：吕人杰
