Marcio Fuzeto Gameiro

• Abstract

  The goal of this research project is to rigorously compute implicitly defined curves and manifolds of solutions of nonlinear equations and to use these solution manifolds to rigorously compute bifurcation of solutions to differential equations. (AU)

  Applications of Computational and Topological Methods to Dynamical Systems, AP.R

• Abstract

  The goal of this research project is to develop rigorous computer assisted methods to study the dynamics of differential equations. The goal is to extend the so-called rigorous continuation method to prove the existence of periodic solutions, homoclinic and heteroclinic orbits, determine the stability of these orbits and to compute invariant manifolds. (AU)

  Rigorous computations in dynamics, AP.R

• Abstract

  The goal of this research project is to understand global properties of PDEs by developing rigorous computational methods to prove existence of periodic orbits, connecting orbits and even chaotic dynamics for PDEs, with the long-term goal of unlocking the secrets hidden within the dynamics of complicated fluid mechanics models such as the Navier-Stokes equations and Rayleigh-Bénard convec…

  Rigorous computations for nonlinear partial differential equations, AP.R

(Only some records are available in English at this moment)

• Abstract

  This project consists in the study of bifurcations in ordinary differential equations and its applications, the study of applied problems in differential equations and computational methods to solve such problems.

  Bifurcations in differential equations and applications, BP.IC

• Abstract

  The goal of this project is to study rigorous computational methods to compute invariant manifolds of differential equations and to apply these methods to some well know ODE models.

  Rigorous computations of invariant manifolds, BP.IC

• Abstract

  The main purpose of this project is the study of Mathematical Analysis, with the goal of giving the students a more profound knowledge of the field and to help them develop their academic and professional careers. The students will present lectures in English, alternating between them. The subjects to be studied are numerical sets (and its properties), basic notions of topology in metric …

  Mathematical analysis and linear algebra with applications, BP.IC

(Only some records are available in English at this moment)

• Abstract

  Persistent homology is a growing area inside computational topology. Recently the researchers have been trying to apply these new topological tools to real world problems, from material sciences to the study of proteins. The protein folding problem concerns in knowing how stable a protein is under the action of proteolysis, that means, how easily a protein breaks into smaller polypeptides…

  Persistent homology and its generators applied to protein folding, BE.EP.MS

• Abstract

  The goal of this project is to study rigorous computational methods to compute connecting orbits in ODEs and use these methods to study heteroclinic bifurcations. A study of the state of the art is proposed alongside the application of the methods in some well known ODE models.

  Rigorous computation of heteroclinic bifurcations in ordinary differential equations., BE.EP.MS

• Abstract

  The goal of this project is to use topological data analysis techniques to analyze complex spatio-temporal data. One of the main tools in topological data analysis is persistent homology, which is essentially a non-linear reduction technique used to significantly reduce the dimension of high-dimensional data while still preserving its essential topological information. The main goal of th…

  Analysis of fluid dynamics data via persistent homology, BE.PQ

(Only some records are available in English at this moment)