MSc. Mathematics in the Institute of Mathematics and Statistics of the University of São Paulo. (Source: Lattes Curriculum)
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In his Master's thesis, the applicant will prove generalizations of a classical result in Operator Theory, namely, that two bounded Fredholm operators on a Hilbert space can be joined by a continuous curve of Fredholm operators if and only if they have the same index. (AU)
The student will learn the basic facts about densely defined unbounded operators on Hilbert spaces, aiming at applying them to describe selfadjoint realizations of the Laplace operator. (AU)
The project deals with the study of the basic concepts in differential topology and their connections with the classical topological methods in nonlinear analysis, as the topological degree theory and the notion of degree of a tangent vector field to a differentiable manifold. These methods will be applied to the study of some differential equations, of first and second order, on manifold…
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