CV Lattes
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Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC) (Institutional affiliation from the last research proposal) Birthplace: Brazil
Associate Professor (MS 5.2) at the Department of Mathematics of the Institute of Mathematics and Computer Sciences (ICMC), University of São Paulo (USP). Bachelor's degree in Mathematics from USP (1988), Master's in Mathematics from USP (1991), PhD in Mathematics from the University of Warwick, UK (1998), Habilitation (Livre-Docência) from USP (2012), and Postdoctoral fellowship at the University of Surrey, UK (2014). Currently a member of two FAPESP Thematic Projects, serving as principal investigator in one of them. Her research focuses on Singularities and algebraic theory in dynamical systems with symmetry; bifurcations with symmetry, reversible and equivariant systems, singularity classification, divergent fold diagrams associated with involutions, simultaneous linearization of involutions, and symmetries in networks of coupled dynamical systems. In teaching, her projects are grounded in the Platonic master-disciple relationship, seeking awareness of the greater good governed by the laws of human nature. (Source: Lattes Curriculum)
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Singularity theory has wide applications to several areas of science such as optics, robotic and computer vision, and interacts with several areas of mathematics, among which we highlight the algebraic geometry and algebraic topology, commutative algebra, differential and affine geometry, the qualitative theory of ordinary differential equations, dynamical systems, and bifurcation theory.…
This project deals with decision-making processes under the formalism of synchronies in networks of coupled dynamic systems. The topic has been addressed in various works, mainly using the Analytic Hierarchy Process (AHP) method. Recently, in 2023, an approach using graphs in networks of coupled systems was established to study decision configurations as bifurcation phenomena arising from…
An involution is a mapping that is its own inverse. The concept of involution is fundamental in group theory and algebras. The interest of this project is to consider involutions under the rich algebraic point of view as well as illustrating its use in solving geometric problems and that are related to discrete dynamical systems. Motivated by the student's interest in algebraic theory, th…
This project deals with the introductory study of dynamical systems, with special interest to coupled dynamical systems, also called networks, given from individual systems (cells) that interact and react according to the laws of coupling. The foundations of this project are the qualitative theory of ordinary differential equations and the algebraic theory of graphs. In general terms, a n…
This project is embedded in a major proposal that includes applications to graph theory to coupled dynamical systems. It provides an introduction to the algebraic theory of graphs applied to dynamical systems, a topic that is rapidly expanding in results and applications during the last twenty years. The studies are directed to the recognition of graphs as a tool in the investigation of n…
The project deals with coupled cell networks, proposing application and advances not only in dynamical systems but also in graph theory and singularities. The relationship between these theories regards the systematic analysis of occurrence of synchrony patterns, which is our main theme of investigation. More precisely, a graph determines the structure of such system, with individual cell…
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The theory of dynamical systems which are equivariant with respect to group actions uses a number of fundamental tools from algebra and topology: group representation theory, invariant theory, normal forms, and singularity and bifurcation theory. Different `flavours' of these are needed to investigate in several directions as, for example, gradient, time-reversible, Hamiltonian and Poiss…
| 1 / 1 | Ongoing grants |
| 2 / 2 | Completed research grants |
| 2 / 2 | Ongoing scholarships in Brazil |
| 13 / 7 | Completed scholarships in Brazil |
| 1 / 1 | Completed scholarships abroad |
| 19 / 13 | All research grants and scholarships |
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