CV Lattes
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Universidade de São Paulo (USP). Instituto de Matemática e Estatística (IME) (Institutional affiliation from the last research proposal) Birthplace: Itália
Graduated in Mathematics from the Università degli Studi di Roma La Sapienza (Italy, 1987), and obtained a Ph.D. in Mathematics from The Pennsylvania State University (USA, 1994), followed by a Habilitation (Livre-Docência) at the University of São Paulo (1998). Currently, he is a Full Professor (MS-6) at the University of São Paulo, a Full Member of the Brazilian Academy of Sciences since May 2012, a member of the Scientific Council of IMPA, a member of the Executive Committee of the IMU International Mathematical Union, and a member of the Mathematics and Statistics Area Coordination at FAPESP.He was awarded the National Order of Scientific Merit (Commander class) in the area of Mathematical Sciences by the Brazilian government in 2018, and received the title of Cavaliere dell'Ordine della "Stella d'Italia" from the Presidency of the Italian Republic in December 2023.He served as President of the Brazilian Mathematical Society (SBM) for three terms, was a member of the Mathematics Area Panel at CNPq, Chair of the Research Committee at IME-USP, member of the Research Council of USP, member of the Special Committee on Work Regimes (CERT) at USP, and member of the Sectorial Evaluation Committee (CAS) for Mathematics and Statistics at the University of São Paulo.His mathematical specialty is Differential Geometry, with research focused mainly on the following areas: Calculus of Variations and Geometric Variational Problems, Bifurcation Theory, Global Riemannian and Lorentzian Geometry, Morse Theory, Symplectic Geometry, and Hamiltonian Systems. (Source: Lattes Curriculum)
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The technique of a priori estimates for solutions of elliptic PDEs is one of the most powerful and widely used tools in the analysis of this class of equations. It enables addressing problems such as the existence and uniqueness of solutions, the equicontinuity of families of solutions in non-compact domains with respect to certain norms, as well as the construction of specific barriers f…
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…
(Only some records are available in English at this moment)
In this project, we intend to study how conformal changes influence the geometry of free boundary minimal surfaces in the Euclidean ball. In addition, we would also like to understand whether it is possible to conclude rigidity results in the conformal class of such surfaces.We also intend to study the geometry of a special type of Riemannian surfaces that admit minimal immersion in three…
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)
Our goal in this project is to study free boundary problems in order to understand the nature of the geometry and topology of their solutions under conformal changes, under curvature gap, and by comparing their geometry and the ambient geometry.
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 grants |
| 52 / 31 | Completed research grants |
| 1 / 1 | Ongoing scholarships in Brazil |
| 25 / 18 | Completed scholarships in Brazil |
| 1 / 1 | Ongoing scholarships abroad |
| 2 / 1 | Completed scholarships abroad |
| 83 / 54 | All research grants and scholarships |
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