Bachelor in mathematics from Università degli Studi di Milano (2003), master in mathematics from Universitá di Pisa (2005), Licenza in Matematica from Scuola Normale Superiore Di Pisa (2005), and Ph. D. in mathematical physics from International School for Advanced Studies (Trieste, 2009). Now "professor adjunto" in the Federal University of São Carlos. Experience in mathematics and mathematical physics, in particular on topology and geometrical structures in string theory. The main research topics are the following ones: generalized cohomology theories and their differential extension, geometry of D-branes, K-theory, gerbes and Gelfand pairs. (Source: Lattes Curriculum)
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The main part of this project concerns differential cohomology theories. The fundamental aim consists of completing the description of these theories and of the corresponding homology theories, underlining the analogy with ordinary cohomology, i.e. with the differential extension of singular cohomology. It is necessary to describe in the proper way the relative, twisted and equivariant ve…
This project aims to study the geometry of algebraic varieties (in particular, affine and projective). Moreover, the candidate will be introduced to Grothendieck's scheme theory. To these ends, category and (pre-)sheaf theories will be used as part of the fundamental language.
The main aim of this project consists in the construction of a natural differential extension of singular homology, dualizing the analogous extension in the framework of cohomology. In particular, the groups we are going to define are supposed to fit in suitable exact sequences, analogous to the cohomological ones. Moreover, we expect that the corresponding version of Poincaré duality hol…
The main aim of the present project consists in introducing the candidate to the theory of finite-dimensional Lie algebras. He will start from the definition of Lie algebra and he will conclude with the classification of simple complex algebras through the corresponding root systems and Dynkin diagrams. Since the concept of representation is particularly relevant in this theory, in the fi…
The main aim of this project consists in introducing the candidate to the fundamental notions of mathematical logic. In particular, he will begin by deepening his knowledge on naive set theory, dealing with von Neumann theory of ordinals and cardinals and with the class of well-founded sets. Afterwards, he will study in detail propositional calculus and first-order theories, both from syn…
The candidate intends to deepen his knowledge on K-theory, considering its various significant versions and their main applications. Moreover, he is going to analyse in detail the construction of the most relevant models of twisted K-theory. In particular, he will concentrate on the model through twisted vector bundles, trying to show directly that it represents a twisted cohomology theor…
The candidate, during his previous bachelor projects, learnt the basic concepts of Algebraic Topology (fundamental group and covering spaces, singular homology and cohomology, first notions about generalized cohomology theories). In this project we are going to study the language of $\infty$-categories, which is essential to understand the classification of topological field theories achi…
(Only some records are available in English at this moment)
The present project is the natural continuation of the one realized by the former Ph.D. student Alffer Gustavo Hernandez Posada, who computed some interesting twisted K-theory groups up to extension, i.e. he showed that they are the central term of a certain short exact sequence. This is a meaningful result, but it has to be completed by computing the groups themselves, not only up to ext…
| 1 / 1 | Completed research grants |
| 3 / 3 | Ongoing scholarships in Brazil |
| 6 / 6 | Completed scholarships in Brazil |
| 1 / 1 | Ongoing scholarships abroad |
| 11 / 11 | All research grants and scholarships |
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