Undergraduate degree in Mathematics at the University La Sapienza, Rome, Italy. Ph. D. In Mathematics at the Pennsylvania State University, USA, 1994. Current position: Professor of Mathematics at the Universidade de São Paulo, Brazil. Member of the Brazilian Academy of Sciences since May 2012. President of the Brazilian Mathematical Society. Member of the International Mathematical Union Executive Committee. Main research interests: Calculus of Variations, Bifurcation Theory, Geometric Variational Problems, Riemannian and Lorentzian Geometry, Morse Theory, Symplectic Geometry and Hamiltonian Systems. (Source: Lattes Curriculum)
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The researchers and students participating in this project to investigate new trends regarding differential geometric methods used in modern theories of Mathematics and Physics. The project program combines research in differential geometry and geometric analysis. Transcending the boundaries of the associated subprojects are a range of modern techniques such as geometric flows, PDE soluti…
This is a research project in the area of Dynamical Systems and Riemannian Geometry that will be carried out by researchers based at the City University of New York, EUA, the Universidade de São Paulo and the Universidade Federal do Estado de São Paulo. Dynamics in ow dimension, transition to chaos, geodesics in manifolds with singular boundary, minimal surfaes, dynamics of the Henon fami…
The main theme of the research proposed in this project will be the study of geodesics in Riemannian or Finslerian compact manifolds with singular boundary. In particular, together with Prof. Piccione, we will study the existence of geodesicsthat connect a point in the interior with a point on the boundary, in the case where the metric degenerates on the boundary with a conformal factor t…
We intend to prove the existence of infinitely many non-planar minimal spheres in sufficiently elongated ellipsoids. (AU)
(Only some records are available in English at this moment)
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…
The goal of the project is the study of fractal geometry using a topological and a dynamical approach. (AU)
In this project, we are concerned with some qualitative properties for solutions to higher order and nonlocal partial differential equations arising in differential geometry. More precisely, we are interested in local asymptotic behavior and multiplicity results for generalizations of the Yamabe and Allen-Cahn equations. (AU)
(Only some records are available in English at this moment)
In this project, we address the study of qualitative properties for some geometric fourth order equations. First, we would like to provide general asymptotic expansions for singular solutions to the Q-curvature equation on the punctured ball with a non-flat background metric. Second, we aim to obtain multiplicity and phase transition results for the fourth order Allen-Cahn-Hilliard equati…
| 2 / 2 | Ongoing research grants |
| 51 / 30 | Completed research grants |
| 25 / 18 | Completed scholarships in Brazil |
| 2 / 1 | Completed scholarships abroad |
| 80 / 51 | All research grants and scholarships |
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