Abstract
Develop research and human resources training activities in the areas of Linear Partial Differential Equations and Multidimensional Complex Analysis. (AU)
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Paulo Leandro Dattori da Silva
CV Lattes
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Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC) (Institutional affiliation from the last research proposal) Birthplace: Brazil
graduation at Licenciatura em Matemática from Universidade Estadual Paulista - UNESP/P.Prudente (1998), graduation at Licenciatura em Ciências from Faculdade de Educação, Ciências e Letras Urubupungá (1994), graduation at Licenciatura Plena em Química from Universidade do Oeste Paulista (1996), master's at Mathematics from Universidade Federal de São Carlos (2001) and doctorate at Mathematics from Universidade Federal de São Carlos (2004). Has experience in Mathematics, focusing on Partial Differential Equations, acting on the following subjects: semi-global solvability, campos vetoriais, resolubilidade global, resolubilidade semi-global and global solvability. (Source: Lattes Curriculum)
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Research grants
- Geometric Theory of PDE and Multidimensional Complex Analysis, AP.TEM
- Global hypoellipticity and solvability on product manifolds, AP.R
Abstract
We propose to investigate global properties of certain systems of partial differential equations of geometric importance, on spaces known as tube structures, or the product manifolds. They areconstitued by systems of vector fields with symmetries that can be studied via Fourier analysis. Our aim is to determine necessary and/or sufficient conditions for their solvability, and for the regu…
- II Parana Symposium on Differential Equations, AO.R
- Solvability and hypoellipticity of first order partial differential operators and boundary value problems, AP.R
Abstract
Let X be smooth, connected, n-dimentional manifold and let \mathcal{L} be a nonsingular smooth complex vector field defined on X.This project deals with the study of problems related with semiglobal/global solvability and global hypoellipticity of equations in the form\mathcal{L}u=Au+B\overline{u}+fdefined in X, where A, B and f are smooth functions.Also, it deals with the study of genera…
- Solvability and hypoellipticity of first order partial differential operators and the Riemann-Hilbert problem, AP.R
Abstract
Let X be smooth, connected, n-dimentional manifold and let L be a nonsingular smooth complex vector field defined on X.This project deals with the study of problems related with semiglobal/global solvability and global hypoellipticity of equations in the formLu=Au+B\overline{u}+fdefined in X, where A, B and f are smooth functions.Also, it deals with the study of generalized Riemann-Hilber…
(Only some records are available in English at this moment)
Scholarships in Brazil
- Sub-Laplacians on compact Lie groups, BP.PD
Abstract
The hypoellipticity ($C^\infty$, analytic and Gevrey, both local and global) of sub-Laplacians has been addressed by several authors, but it is still a problem with many unresolved questions, since no necessary and sufficient conditions are known to characterize the hypoellipticity of a sub-Laplacian in its general form. We propose a new line of investigation: the global hypoellipticity a…
- Levi-flat CR structures and comparison principles, BP.PD
Abstract
This research project deals with a correspondence between Levi-flat CR structures and systems of real vector fields. In several different models, this correspondence allows to obtain results about vanishing of cohomology spaces, global solvability and global hypoellipticity of one of the structures from information about the other. In presence of a Lie group action, the naturally associat…
- Tube type structures on compact Lie groups, BP.DR
Abstract
This project deals with the global solvability and global hypoellipticity of operators given by tube-type structures defined on product manifolds of the form MxG, where M is a smooth compact manifold and G is a compact Lie group. This project also forecast the approach of this subject both in the context of functions of class C^\infty, and in the context of ultradifferentiable functions (…
- Partial Differential Equations: an approach via Distribution Theory, BP.IC
Abstract
This research project deals with the study of linear partial differential equations via Distribution Theory. More specifically, our goal is to study the existence and regularity of local solutions of PDE's of the form Pu=f, where f is in C^\infty(\mathbb{R}^n), and P is given in the formP=\sum_{|\alpha|\leq m}a_\alpha\partial_x^\alpha, a_alpha\in\mathbb{C}.
- Local solvability of rotationally invariant differential forms, BP.MS
Abstract
We will deal with local solvability of classes of linear partial differential operators. More precisely, we will deal with solvability of classes of first order differential equations in context of differential forms. Let \Omega=A(z)dz+B(z)d\bar{z} be a smooth differential 1-form defined in a neighborhood of the origin in \mathbb{R}^2. We say that \Omega is rotationally invariant if \Om…
(Only some records are available in English at this moment)
Scholarships abroad
- Global properties of systems of vector fields on compact Lie groups, BE.EP.DR
Abstract
Systems of vector fields arise as a local basis of an involutive sub-bundle $\mathcal{V}$ of the complexified tangentbundle $\mathbb{C}T\mathcal{M}$. Examples of involutive structures $(\mathcal{M},\mathcal{V})$ include foliations, complex structures, and CR structures.In this project we will investigate global properties of involutive structures defined on a smooth manifold $M$. Many res…
- Solvability for a class of first-order partial differential operators, BE.PQ
Abstract
Let X be a two-dimensional, conected, smooth manifold and let L be a nonsingular complex vector field, with smooth coefficients, defined on X. This project deals with the study of problems related to global and semiglobal solvabitity of equations in the form Lu=Au+f defined in X, where A and f are smooth functions. Also, this project deals with the Riemann-Hilbert problem with equationLu=…
Total / Available in English
| 2 / 2 | Ongoing grants |
| 7 / 5 | Completed research grants |
| 2 / 2 | Ongoing scholarships in Brazil |
| 13 / 11 | Completed scholarships in Brazil |
| 1 / 1 | Ongoing scholarships abroad |
| 1 / 1 | Completed scholarships abroad |
| 26 / 22 | All research grants and scholarships |
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