Undergraduate course in Mathematics at Universidade Federal do Rio Grande do Sul (2014), Master in Mathematics (Geometry) at the same university (2017) and Doctor of Science (Mathematics) at University of São Paulo (2021). My research interests are Differential Geometry and Geometric Analysis. More specifically, I study problems in the area of Spectral Geometry. (Source: Lattes Curriculum)
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This project aims to study certain eigenvalue optimisation problems in Riemannian manifolds. Firstly, we would like to prove the existence of extremal domains for the first eigenvalue of the Laplacian in complete, noncompact and geometrically bounded manifolds. Secondly, we intend to show that the presence of symmetries in a manifold prevents the existence of extremal metrics which are i…
We will study two classical topics that are at the origin of Algebraic Topology: the fundamental group of a topological space and covering spaces. We will begin with the formal description of the fundamental group of a space and examine some of its properties. Then, we will describe this group in the case of the circle, which, together with the Van Kampen theorem, will allow us to compute…
We will study three classical fixed point theorems: Banach, Schauder and Kakutani. To do this, it will be necessary to establish a solid foundation on the theory of Metrics Spaces and Functional Analysis, areas any mathematician -- pure or applied -- has to be familiar with. As applications of these results, we will explore the classical theorem of existence and uniqueness of ordinary dif…
From the study of differentiable manifolds, central objects in differential geometry, the student will develop the necessary tools to prove Stokes' theorem on manifolds-a statement about the integration of differential forms-obtaining the important corollaries that follow. In the second half of the project, the intention is to enter and become familiar with Riemannian geometry, aiming to …
We intend to extend the theory of critical metrics for the first eigenvalue of the Laplacian developed by El Soufi and Ilias in two directions: to consider this functional restricted to the class of metrics induced by embeddings into a fixed ambient manifold, and also to consider the other eigenvalues in this setting. Moreover, we intend to study the spectral geometry of surface bundles o…
We seek to extend the application of the techniques of closed minimal surfaces to the case where they are noncompact and have a boundary, and to explore bifurcation phenomena related to these surfaces in homogeneous 3-manifolds. More specifically, we intend to address the following topics: possible elaboration of a survey about homological systoles in Riemannian manifolds, with the propos…
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We intend to apply the techniques of bifurcation theory to prove local and global results concerning the existence of bifurcation minimal tori in Riemannian 3-manifolds which are products of a fixed closed surface and a circle of variable radius. Moreover, we will address the problems of giving examples and possibly characterizing extremal domains and surfaces for the first eigenvalue of …
| 1 / 1 | Ongoing grants |
| 2 / 2 | Ongoing scholarships in Brazil |
| 4 / 4 | Completed scholarships in Brazil |
| 1 / 1 | Completed scholarships abroad |
| 8 / 8 | All research grants and scholarships |
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