CV Lattes
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Universidade Federal de São Carlos (UFSCAR). Centro de Ciências Exatas e de Tecnologia (CCET) (Institutional affiliation from the last research proposal) Birthplace: Brazil
bachelor's at Licenciatura em Matemática from Universidade Estadual Paulista Júlio de Mesquita Filho (2004), master's at Mathematics from Universidade de São Paulo (2007) and doctorate at Mathematics from Universidade de São Paulo (2009). Has experience in Mathematics, focusing on Defferential Geometry, acting on the following subjects: torção analítica, teorema de cheeger-müller, torção de reidemeister. (Source: Lattes Curriculum)
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This project is a continuation of the thematic projects 00/05385-8, 04/10229-6, 08/57607-6, 12/24454-8, 16/24707-4 and aims to develop research in Algebraic, Geometric and Differential Topology and Topological Data Analysis. The project consists in the training of human resources in the project's research lines, qualified scientific production and scientific visits both by foreign researc…
Since the famous Index Theorem of Atiyah and Singer, the relation between tools from different areas of Mathematics has applications in different lines of research. We propose the investigation of geometric/analytical elements of manifolds and pseudomanifolds, such as spectral invariants and geometric analysis. This project is a continuation of FAPESP Project 2018/23202-1. (AU)
We propose to do research in two questions of a topological nature that arose from the study of complex structures on manifolds with conical singularities. Both questions (pertaining to classifying spaces and tensor products) are motivated by the same principle that underlies non-commutative geometry: knowing a lot about an object (for instance topological), and having another of a differ…
We propose the study of the spectral geometry and the geometric/analytic elements involved in spectral invariants of singular spaces with the aim to obtain a geometric/topological description of this invariant. We still propose the study of these invariants in an abstract context. (AU)
(Only some records are available in English at this moment)
We propose to investigate torsion invariants, such as Whitehead Torsion and Reidemeister Torsion, in G-spaces, that is, spaces with an action of a finite group G that is not necessarily free. (AU)
We propose the study of some classical theorems in Topology such as the Tychonoff Theorem, Urysohn's Lemma, Tietze's Extension Theorem, and Ascoli's Theorem. These fundamental elements are key points in various areas such as Algebraic Topology, Analysis, and Geometry
We propose to investigate combinatorial invariants such as, for example, the Reidemeister (or Whitehead) Torsion, for pseudomanifolds with positive-dimensional singular sets. We will then explore a construction of such invariants for homotopically stratified manifolds.
(Only some records are available in English at this moment)
We propose an in-depth study of Morse Theory, focusing on the Fundamental Theorem of this theory. To this end, we will explore essential tools from Riemannian Geometry and Algebraic Topology, which are fundamental for understanding the Fundamental Theorem of Morse Theory.
In this research project, we will consider functionals related to mean curvature flow in an ambient space which evolves by an extended Ricci flow from the perspective introduced by Lott when studying mean curvature flow in a Ricci flow background. Mainly, the functional we will focus on is the Gibbons-Hawking-York action on Riemannian metrics in compact manifolds with boundary. We will co…
We propose a introductory study about analytic number theory with the aim to explore results related with the distribution of the prime numbers.
(Only some records are available in English at this moment)
This project aims to study quantum invariants of 3-manifolds arising fromTopological Quantum Field Theories (TQFTs), following the foundational work ofReshetikhin and Turaev. These TQFTs are constructed from modular categories-algebraic structures that contain simple objects, a braiding, a twist, and a duality-providing the necessary data to define topological invariants of closed 3-manif…
We will consider functionals related to mean curvature flow in an ambient space which evolves by an extended Ricci flow. Mainly, the functional we will focus on is the Gibbons-Hawking-York action on Riemannian metrics in compact manifolds with boundary. We will compute its variational properties to the analysis of its time-derivative under Perelman's modified extended Ricci flow. In this …
We propose the study of surfaces with asymptotically cusps ends with the aim to present the full asymptotic expansion of the heat kernel trace and to present uniformization results following the works of B. Osgood, R. Philips and P. Sarnak.
| 1 / 1 | Ongoing grants |
| 7 / 7 | Completed research grants |
| 4 / 4 | Ongoing scholarships in Brazil |
| 10 / 9 | Completed scholarships in Brazil |
| 2 / 2 | Ongoing scholarships abroad |
| 1 / 1 | Completed scholarships abroad |
| 25 / 24 | All research grants and scholarships |
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