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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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…
The projets addresses several topics in differential geometry and geometric analysis, including: 1) group and groupoid actions in riemannian and pseudo-riemannian manifolds; 2) submanifold theory, minimal submanifolds and constant mean curvature hypersurfaces; 3) variational calculus and global analysis in riemannian, sub-riemannian and pseudo-riemannian geometry, with applications to gen…
We intend to prove the existence of infinitely many non-planar minimal spheres in sufficiently elongated ellipsoids. (AU)
We propose the study of five topics related to the classification of manifolds endowed with a Riemannian metric and some other compatible structure, such as (a) a gradient holomorphic geodesic field; (b) harmonic curvature tensor; (c) parallel distribution with compact flat leaves. (AU)
(Only some records are available in English at this moment)
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)
We intend to use techniques from global analysis on manifolds (Morse Theory, Lusternik-Schnirelman theory, Bifurcation Theory) to determine multiplicity of solutions of geometric variational problems. (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…
| 3 / 3 | Ongoing research grants |
| 49 / 28 | Completed research grants |
| 24 / 17 | Completed scholarships in Brazil |
| 1 / 1 | Ongoing scholarships abroad |
| 1 / 0 | Completed scholarships abroad |
| 78 / 49 | All research grants and scholarships |
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