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
graduate at Bacharelado em Matemática from Instituto de Matemática e Estatística (2003), master's at Mestrado em Matemática from Instituto de Matemática e Estatística (2005) and ph.d. at Doutorado em Matemática from Instituto de Matemática e Estatística (2009). Has experience in Mathematics, acting on the following subjects: independence, discrete subspaces, and trees. (Source: Lattes Curriculum)
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The area of graphs is a central area in combinatorics - mainly in finite combinatorics. In the infinite case, infinite combinatorics often gets mixed with set theory and graphs remain an important part. In general, the problems and techniques used in infinite graphs are inspired by their finite versions, but this does not mean that set theory problems and techniques cannot interact. This …
It is not uncommon in mathematics that solutions of problems have some combinatorical step - even when the problem's statement does not indicate such connection. It is also not uncommon that problems of combinatorical nature to have in their solution some tool of another field - as topology or set theory. This project aims the study of several problems that have some kind of connection wi…
This project mainly tries to proceed in some researches lines that the author has been developing in the past few years. One of the central problems is the Michael's problem (if the space of the irrationals is productively Lindelöf) but other problems involving preservation of proprierties in the product are also among the main goals of this project. (AU)
(Only some records are available in English at this moment)
This project aims to study the concept of flows in graphs. This is a concept that has its origins in applications but has also proven to be quite fruitful in the theory. The project aims to present some classical results from the literature as well as a first contact with current problems.
Infinite combinatorics is a mathematical field that includes several areas, and has aplications in several others. In this project, we will focus on the study of results on infinite graphs. We will also continue to study the tools used while studying the cycle double cover conjecture and its generalization, the faithful cycle cover conjecture, that started during undergrad, issuing also o…
This Doctoral Scholarship Proposal is a natural extension of a previous FAPESP Master research project carried out by the applicant and his supervisor, which yielded one published paper and two preprints under elaboration. Through grant number 2021/13373-6, they worked with different branches of Infinite Graph Theory, a subarea of combinatorics still being developed abroad and with few re…
This postdoctoral research project aims to further develop the researcher's performance in Set Theory and General Topology, nationally and internationally, with support from an international research network. The main topics of research are: almost disjoint families, Isbell-Mrówka spaces, countably compact topological groups, weakenings of normality and compactness, cardinal characteristi…
The main objective of this project is to answer set-theoretic questions about Borel and measurable colorings of graphs relevant to (1) ergodic theory; (2) hyperbolic geometry; (3) computability and (4) dynamical systems. The main technique that we may employ is iterated forcing of notions that satisfy Axiom A. If the objectives are achieved, we will have contributed to expanding the front…
This research project aims to study properties of infinite graphs via tools developed by Graph and Set Theories to deal with the Unfriendly Partition Conjecture, trivial in the context of graphs with finite set of vertices but rich when formulated in a general scenario.Although presented as a simple question related to graph colouring, the comprehension of the results developed so far abo…
(Only some records are available in English at this moment)
The combinatorial and topological properties of end spaces have been explored by an extensive bibliography within infinite graph theory. On the other hand, the edge-related counterpart to these structures does not benefit from such a well established literature. In fact, besides a first article due to Hahn, Laviolette and Sirán, almost no other reference brings a deeper investigation abou…
The main objective of this research stay is to answer set-theoretic questions about Borel and measurable colorings of graphs relevant to geometry and dynamical systems. The main technique that we may employ is iterated forcing of notions that satisfy Axiom A. If the objectives are achieved, we will have contributed to expanding the frontiers of set theory.
This project aims to complement the student's formation by advancing the research started in a paper submitted by the student and the advisor in 2019 in the field of topological games and selection principles, as well as attacking classical open problems in the theory of D-spaces and exploring a new way of connecting infinite games to category theory. (AU)
| 6 / 6 | Completed research grants |
| 3 / 3 | Ongoing scholarships in Brazil |
| 15 / 15 | Completed scholarships in Brazil |
| 1 / 1 | Ongoing scholarships abroad |
| 2 / 2 | Completed scholarships abroad |
| 27 / 27 | All research grants and scholarships |
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