Research program

Singularity Theory, Topology and Geometry

From the local Euler obstruction to the topology of singular dynamical systems — a path of more than twenty years in the geometry and topology of singular spaces, with collaborations in Brazil, France, the United States, Spain, and Mexico.

Research lines

Research areas

01

Topology of Singularities

Characteristic classes of singular varieties, invariants, and intersection homology.

02

Topological Dynamics

Conley index theory for Gutierrez–Sotomayor flows on singular manifolds.

03

Algebraic Geometry

Divisorial geometry and invariant theory.

04

Racial and Ethnic Relations

Racial literacy, research on Black communities and racial equity.

Funding

Research projects

Completed funding
2019 – 2026

New Frontiers in Singularity Theory

FAPESP Thematic Project. Principal investigator.

2019 – 2021

PROBAL CAPES-DAAD — Topology and Geometry of Determinantal Singularities

Brazil–Germany cooperation. Coordinator. Collaborators: Maria Aparecida Soares Ruas, João Nivaldo Tomazella, Thaís Maria Dalbelo, Miriam da Silva Pereira, Anne Frühbis-Krüger, Wolfgang Ebeling, Duco van Straten, among others.

2017 – 2018

USP-COFECUB — Topology and Geometry of Singularities

Cooperation with the Singularities group at Aix-Marseille Université. Coordinator.

2013 – 2016

CNPq Universal Project — Topological Study of Singularities

Six subprojects, ranging from stable mappings to invariants on toric varieties. Coordinator.

2011 – 2022

CNPq Research Productivity Fellowship (PQ-2)

Renewed across successive individual research project cycles.

International network

International Research Network

Postdoctoral fellowships, cotutelle agreements, and international cooperation projects have built an active network of scientific collaboration over more than twenty years.

2023 – 2024

Postdoctoral fellowship — Universitat de València

Spain · FAPESP funding

2016 – 2017

Postdoctoral fellowship — Northeastern University

Boston, USA · FAPESP funding

2011 – 2012

Postdoctoral fellowship — Aix-Marseille Université

France · CNPq funding

2003 – 2007

Cotutelle doctorate — USP & Université de la Méditerranée

Marseille, France · advisors Maria Aparecida Soares Ruas and Jean-Paul Brasselet

Frequent collaborators include researchers in Brazil, France, Spain, Mexico, and the United States. The network also supports ongoing proposals for cooperation with African partners (CNPq/MCTI PROAFRICA) and the formation of a national research network (CNPq/FNDCT Universal).