Ohio State is in the process of revising websites and program materials to accurately reflect compliance with the law. While this work occurs, language referencing protected class status or other activities prohibited by Ohio Senate Bill 1 may still appear in some places. However, all programs and activities are being administered in compliance with federal and state law.

Grad Student Seminar - Yilong Zhang

Yilong Zhang
October 2, 2018
5:15 pm - 6:15 pm
Cockins Hall 240

Title: The Topology of Complex Hypersurface Singularities

SpeakerYilong Zhang (Ohio State University)

Abstract: Let $f(z_1,...,z_n)$ be a polynomial function in $n$ complex variables, so the zero locus of $f$ defines a hypersurface $X$ of $\mathbb C^n$. Assume that $p$ is an isolated singularity of $X$. We want to understand the topology of $X$ around the singularity $p$. Let $S_r\subset \mathbb C^n$ be a $2n-1$-sphere with radius $r$ centered at $p$, whose intersection with $X$ is a smooth. Milnor showed that for sufficiently small $r$, the map $z\mapsto f(z)/|f(z)|$ from $S_r\setminus X$ to the unit circle is a smooth fiber bundle, and the fiber $F$ is commonly called the Milnor fiber, which has homotopy type a bouquet of $n-1$-spheres. The purpose of this talk is to give an introduction to the Milnor fiber, and I will explain how it is related to stable reduction of algebraic curves.

Events Filters: