CV Lattes
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Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica (IMECC) (Institutional affiliation from the last research proposal) Birthplace: Brazil
Electronic engineer from Instituto Tecnológico de Aeronáutica (1989), master's on Mathematics from Universidade Estadual de Campinas (1992) and PhD. on Mathematics from University of Warwick, UK (1995). Experience in dynamical systems, focusing on the intersection of stochastic analysis, geometry and control. Director of the Institute of Mathematics, Statistics and Computer Science (Imecc-UNICAMP) from 2018-2022. (Source: Lattes Curriculum)
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This project concerns the application of the Institutional Technical Funding of the Institute of Mathematics, Statistics and Scientific Computing - IMECC, UNICAMP. We propose to use these resources to instal air conditioning in the Annex I building, occupied by the Institute's postgraduate students. (AU)
Our research group in Mathematics Department -- UNICAMP focus on the study of intertwined properties of stochastic analysis, geometry and dynamical systems, mainly concerning the theory of continuous time semimartingales (e.g., Brownian motion), and more recently including jumps (e.g., Lévy processes). This project, which connects researchers who use common techniques on probability and e…
These theoretical studies will be intimately connected with the investigation of experimental and natural dynamical networks of increasing complexity starting from a few coupled lasers, via hybrid networks of neurons to the system Earth. The latter one is a special challenge for the network theory and it will be a focus of this project. A main topic will be the understanding of the functi…
(Only some records are available in English at this moment)
The project intends to bring up an international level mathematician on stochastics and rough path theory. The initial stage of the process require familiarization with the analysis involved in these equations, with differential geometry an processes on fibre bundles. Within this area the thesis of the project is a response to the following problems (giving emphasis on the first or the la…
Study dynamics and geometry in foliated spaces via stochastic calculus in foliation. In this context, relate: stability in the sense of Lyapunov exponents of a brownian clad motion, foliated approximation, relation with curvature, geometric entropy and dynamic entropy. (AU)
This project aims to study recent results in the literature about the connection between positive definite kernels and concepts from probability, such as metrics in this space, independence and conditional independence. For this purpose, it is used the reproducing kernel Hilbert space of a positive definite kernel in order to obtain a semi-inner product on the space of measures with bound…
We will study the decomposition of stochastic flows into a differentiable manifold and use the decomposition to obtain a kind of averaging principle. We will also study the existence and uniqueness of the nonlinear stochastic transport equation.
This project aims to study the Weierstrass semigroup and Weierstrass pure gaps of a family of algebraic curves containing Hurwitz and Fermat curves.
(Only some records are available in English at this moment)
We propose the study of a system of particles with moderate mean-field interactions and subject to a common noise. We derive the asymptotic behavior ofthe population, which gives rise to a McKean-Vlasov SDE and an associated stochastic PDE at the density level. We investigate the well-posedness and uniqueness of both equations and explore the quantitative convergence of the empirical meas…
Stochastic partial differential equations model physical phenomena in the presence of noise. The exact nature of the noise may vary, leading to a plethora of mathematical tools developed for their treatment. This proposal is built around two lines of research, captured by two conjectures, which are distinct, yet deeply intertwined. Both refer to the 2D stochastic Navier--Stokes equations …
Characterization of bifurcation in Markovian systems using the process of n-points, as in Kunita "Stochastic Flows and Stochastic Differential Equations", C.U.P. An average principle in Hamiltonian systems via decomposition of flows in a foliated manifold. Conjugacies of stochastic flows with random systems (cohomologies) that preserve tensor fields. (AU)
(Only some records are available in English at this moment)