Morse-Conley Theory, Singular Varieties, and Intersection Homology

• Grant number: 23/17645-6
• Support Opportunities: Scholarships abroad - Research
• Start date: May 06, 2024
• End date: August 02, 2024
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Dahisy Valadão de Souza Lima
• Grantee: Dahisy Valadão de Souza Lima
• Host Investigator: Jean-Paul Michel Ildephonse Brasselet
• Host Institution: Centro de Matemática, Computação e Cognição (CMCC). Universidade Federal do ABC (UFABC). Ministério da Educação (Brasil). Santo André , SP, Brazil
• Institution abroad: Aix-Marseille Université (AMU), France
• Associated research grant: 19/21181-0 - New frontiers in Singularity Theory, AP.TEM

Abstract

The study of singular varieties and continuous flows over such structures is an area of high relevance, finding applications in various fields, including Theoretical Physics and Computational Imaging, among other scientific spheres. This project focuses on the application of Conley Theory to GS flows on singular varieties, investigating possible connections between Morse-Conley Theory and Intersection Homology.Topological analysis of singular varieties represents a promising research line, especially when dealing with challenges presented by spaces lacking smoothness. The integration of Conley Theory with Intersection Homology offers a robust and comprehensive approach to understanding and characterizing these phenomena.By employing Singularity Theory, our proposal aims not only to expand but also to consolidate the existing theoretical framework. It is expected that this approach will provide more precise and effective mathematical tools, enabling the attainment of more solid results in this area.