BIMSA > Seminar on Algebraic, Complex Geometry and Singularities Finite Determinacy on Formal Power Series
Finite Determinacy on Formal Power Series
Organizer
Shing Toung Yau
Speaker
Shuanghe Fan
Time
Friday, November 1, 2024 8:00 PM - 9:00 PM
Venue
Online
Abstract
In singularity theory, finite determinacy helps to classify singularities by determining if a singularity is entirely defined by its Taylor expansion up to a certain order. We extend the classical finite determinacy theorem from convergent power series rings to formal power series rings over an arbitrary field by higher order Jacobian matrix theory. The main results in this talk include: 1. A novel approach to finite determinacy for formal power series over an arbitrary field, which is a more refined judgment method for finite determinacy than the existing result offers. 2. Computational techniques for related expressions involving both automorphisms and invertible elements. 3. Discussing cases facilitating the transformation of a system of power series into a system of polynomials. The talk will delve into the main theorems, explaining the concepts, their significance, and providing illustrative examples.