Singularities, Characteristic Classes, and Hodge Structures

• Grant number: 25/06178-3
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Start date: September 02, 2025
• End date: October 11, 2025
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Nivaldo de Góes Grulha Júnior
• Grantee: Nivaldo de Góes Grulha Júnior
• Visiting researcher: Jean-Paul Michel Ildephonse Brasselet
• Visiting researcher institution: Centre National De La Recherche Scientifique/Cnrs, France
• 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

The study of characteristic classes in singular spaces has established itself as one of the most active fields in contemporary mathematics, providing powerful tools for understanding the geometric and topological structure of singular varieties. In this context, the interplay between intersection homology, characteristic classes, and mixed Hodge structures has unveiled new perspectives and significant applications.This project, to be developed in collaboration with Professor Jean-Paul Brasselet, focuses on the investigation of fundamental invariants such as the local Euler obstruction, Milnor classes, and the characteristic classes of toric varieties from this new perspective.During his seven-week stay in Brazil, Professor Jean-Paul Brasselet will offer a short course on characteristic classes and Hodge structures, as well as seminars on recent advances in the field.The approach adopted in this project combines classical methods from topology and algebraic geometry with modern techniques from the theory of mixed Hodge structures and singularity theory, fostering a dialogue between different areas of mathematics.The expectation is to obtain high-impact results, contributing to the development of new theoretical tools and applications in the study of singularities, while also expanding the reach and visibility of research in this area both nationally and internationally. (AU)