An introduction to Milnor's theory

• Grant number: 23/04888-8
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: May 01, 2023
• End date: June 30, 2024
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Maria Aparecida Soares Ruas
• Grantee: Arthur Garcia Tonus
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Associated research grant: 19/21181-0 - New frontiers in Singularity Theory, AP.TEM

Abstract

In this project, we propose to study the topology of complex functions with isolated singularity defined on subsets of C^n through numerical invariants associated to them. We will discuss alternative ways to compute these invariants, using, in particular, the Software SINGULAR.We will use as a basic reference the book Singular points of complex hypersurfaces, by John Milnor. The student already has basic prerequisites of algebraic topology necessary for the development of the project.