CV Lattes
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Universidade Federal do ABC (UFABC). Centro de Matemática, Computação e Cognição (CMCC) (Institutional affiliation from the last research proposal) Birthplace: Brazil
graduate at Matemática from Universidade de Brasília (2008). (Source: Lattes Curriculum)
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In this project, we propose scientific problems related to the study of dynamical systems via Conley Index Theory and to the study ofFloer Homology via Microlocal Sheaf Theory. In the dynamical setting, we want to explore the dynamical effects of spectral sequence analysis for Morse-Smale flows in order to detect cancellations and reductions of periodic orbits. For a more general flow, wi…
In this project , we propose to develop Conley's theory in the context of Morse-Bott and Morse-Novikov flows, associated to Morse-Bott and Morse circular functions, respectively. More specifically, we intend to use the algebraic theory of spectral sequences together with connection matrices to study continuation properties of these flows. We want to associate the topology of the manifol…
In this project we will adopt a Morse-Witten approach via Conley index theory to associate the topology of the manifold to the trajectories connecting critical points of a gradient flow which define the moduli spaces. Some of these flow connections are registered in the integer entry connection matrix. We will study the connection and transition matrices which appear in the Sweeping Algor…
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…
Morse theory features very prominently in modern mathematical physics, specifically the Fukaya category of Lagrangian submanifolds of a symplectic manifold, and in the theory of generating functions of Legendrian submanifolds of a first jet bundle. These two examples have overlap: the Lagrangian conormal of a knot in three-space defines a Legendrian submanifold of the contact unit cospher…
| 1 / 1 | Completed research grants |
| 2 / 2 | Completed scholarships in Brazil |
| 2 / 2 | Completed scholarships abroad |
| 5 / 5 | All research grants and scholarships |
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