Topology of polynomial maps through their bifurcation locus

• Grant number: 23/09684-1
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: November 01, 2023
• Status: Discontinued
• Field of knowledge: Physical Sciences and Mathematics - Mathematics
• Principal Investigator: Francisco Braun
• Grantee: Rodrigo Thomaz da Silva
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil
• Associated research grant: 19/07316-0 - Singularity theory and its applications to differential geometry, differential equations and computer vision, AP.TEM
• Associated scholarship(s): 24/06739-2 - The bifurcation locus of polynomial maps, BE.EP.DR

Abstract

This project aims to study the bifurcation set of a real polynomial function in two real variables and also its connections with other mathematical problems. The project is divided into four main parts: the bifurcation set and its characterization in terms of vanishing and splitting at infinity phenomena, the relation with Jacobian problems, the relation with foliations of the plane and Lipschitz equivalence of real and complex polynomial functions.