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
graduation at Bacharelado Em Física from Universidade de São Paulo (2004) and doctorate at Nonlinear Dynamics from University of Potsdam (2007). Has experience in Mathematics, acting on the following subjects: networks, applied math, caos, sincronizacao and random matrix theory. (Source: Lattes Curriculum)
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This grant addresses challenges posed by real-world complex systems described as networks of interconnected dynamical elements. These systems feature in diverse fields such as ecology, biology, and physics. Changes in the interaction structure have far-reaching effects. Indeed, disorders like Parkinson's disease, schizophrenia, and epilepsy are believed to be linked to abnormal interactio…
The focus of this proposal is the transfer of mathematical knowledge to other areas of science, technology and industry, through a structured research center specially tailored for this purpose. All mathematical knowledge is ultimately applicable, if not directly, through other areas of knowledge. In some areas the application of mathematics is almost immediate. However, the practical imp…
The main aim of this project is to develop a mathematical theory for three key aspects of networks, namely, (i) embedding of networks in communicability space, (ii) generalization of random spatial networks to include shape variation, and (iii) mathematical theory of long-range interactions on networked systems. These include important aspects of dynamics on networks such as synchronizati…
This proposal addresses the problem of predicting the occurrence of sudden changes of behaviour in complex systems from data. Such abrupt changes in behaviour are known as critical transitions and are observed in ecology, neuroscience, medicine, and technology. The traditional mathematical theory fails to address these novel challenges, as these complex systems have a wild global behavi…
In a series of recent works, we and our collaborators gave empiric and numerical evidence that the non-ergodicity of a chaotic Hamiltonian system must universally lead to the sustained growth of the entropy of the system and, as a consequence, to the exponential growth of energy at a slow periodic oscillation of parameters. The goal of the project is to build a mathematically rigorous the…
(Only some records are available in English at this moment)
his undergraduate research project aims to introduce undergraduate students to basic results in dynamical systems and complex networks. The student will become familiar with common questions in the field and learn how to approach them using computer simulations. Additionally, the student will take their first steps in understanding the calculation of elementary properties of coupled phase…
This research project explores the connection between ergodic theory and normal numbers. A real number is normal in a given base if its digits exhibit uniform statistical behavior. Ergodic theory provides a powerful framework to study normality. In this project, we investigate classical results such as Weyl's criterion and examine how ergodicity of certain dynamical systems can be used …
(Only some records are available in English at this moment)
The study of random dynamical systems is extremely relevant for modeling and understanding several natural systems (climate dynamics and certain classes of dynamic programming problems, for example). This project aims to study random dynamical systems from the perspective of iterative function systems. To this end, the project is divided into four periods, beginning with the construction …
A network encodes a structure of individual units (the nodes), together with the information of how these units depend on each other. We project focus on qualitative changes in the dynamics of networks as one or more parameters vary. One can, for example, think about the emergence of steady state points or periodic orbits, or the phenomenon where by multiple cells in a network start displ…
This project aims to develop the relevant mathematical basis to the reconstruction of the dynamics of dynamical systems from a dataset using the Sparse Recovery technique. For this purpose, the project is divided into three stages, which include the study of the properties and applications of the Hilbert Transform in signal processing, the understanding and simulation of Rössler's attract…
(Only some records are available in English at this moment)
This proposal aims to develop a rigorous dimension reduction principle for dynamical systems coupled on complex networks by comparing the low-degree-node dynamics against a reference random dynamical system (RDS). A recent breakthrough due to Pereira, van Strien, and Tanzi proved the dimension reduction for a special class of heterogeneously coupled maps, relying crucially on global hyper…
The main goal of the present project is to investigate the effects of large delay on the synchronization of delay coupled networks: very few results have been rigorously proved in this direction. Moreover, most efforts in the field have tackled the case when the synchronized dynamics does not depend on the delay. In this project, we will tackle the case where the delay influences the sync…
| 2 / 2 | Ongoing grants |
| 8 / 6 | Completed research grants |
| 6 / 6 | Ongoing scholarships in Brazil |
| 10 / 10 | Completed scholarships in Brazil |
| 2 / 2 | Completed scholarships abroad |
| 28 / 26 | All research grants and scholarships |
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