CV Lattes
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Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica (IMECC) (Institutional affiliation from the last research proposal) Birthplace: Brazil
Bachelors degree in Mathematics (2001) and Masters in Applied Mathematics (2002) from the Federal University of Rio de Janeiro (UFRJ), Masters in Theoretical Physics from the University of Cambridge (2004), and PhD in Mathematics from Imperial College London (2009), supervised by Sir Simon K. Donaldson. Has experience in Differential Geometry, Geometric Analysis, Algebraic Geometry, Nonlinear Partial Differential Equations, and Mathematical Physics, with a focus on gauge theory, special geometric structures on manifolds, and their associated geometric flows. Also interested in string theory/M-theory, information theory, and applications of artificial intelligence to Mathematics. Currently serves as Vice-Director of the CBG Brazilian Centre for Geometry and Scientific Business Manager at BI0S Brazilian Institute of Data Science. (Source: Lattes Curriculum)
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The Brazilian Institute of Data Science (BI0S) is a research center with the main purpose to develop state-of-the-art solutions in data science and artificial intelligence (AI), solving relevant problems and connecting academia, companies, startups, society and the public sector in an integrated innovation ecosystem. It will contribute to scientific, technological and social development, …
This project stands at the crossroads of complex algebraic geometry and Riemannian geometry to put together a team of Brazilian and French experts from both disciplines with a common goal: enhance our understanding of the interplays between algebraic invariant theory and special connections on bundles and build a transatlantic research group ready to weigh in on the new challenges of Geom…
Gauge theory is the study of differential equations involving connections on vector bundles over manifolds using methods from differential geometry, algebraic geometry and geometric analysis. This is area of research emerged in the late 1970s, especially after works by Michael Atiyah, Nigel Hitchin and simon Donaldson, among others, as a mathematical model for classical field theory in ma…
The applicant will study a number of problems in the context of gauge theory in dimensions higher than 4 and the construction of special geometric structures and submanifolds. In particular, one shall address certain advances towards an analogous to Donaldson-Thomas theory for moduli spaces of generalised instantons over G2-manifolds, and the characterisation of G2-structures with 'little…
(Only some records are available in English at this moment)
Riemannian geometry is one of the most impactful domains in mathematics, being essential for the description of spacetime in General Relativity and widely used across fields such as economics, biomedicine, data science, and computer graphics. The classification of Riemannian manifolds, completed by Berger, highlights seven classes of holonomy groups, including Calabi-Yau and $G_2$ varieti…
This project proposes a, partially original, investigation into the topic of geometric structures, viewed as stabilized tensors by a reduced structure group, following the unifying approach presented by Daniel Fadel, Eric Loubeau, Andrés J. Moreno, and Henrique N. Sá Earp in 2024. The goal is to obtain Taylor formulas for tensors associated with Spin(7)-structures and U(m)-structures, ana…
The student will systematically and rigorously study the foundations of differential geometry that underpin the mathematical formulation of general relativity. (AU)
(Only some records are available in English at this moment)
We study the geometry and gauge theory of G2 manifolds with conical singularities, and those have collapsing circle fibers. Our goal is to produce examples, both of these manifolds and instantons on them, clarifying the relationship between the singular limit and the G2-manifolds resolving these singularities. (AU)
This project aims to study the existence of complex and quasi-complex structures in unitary spheres and their relationship with parallelizable unitary spheres. It is also intended to study the historical development of Hopf's problem about the existence of a complex structure in S6. The materials used as a reference will be the articles "A Note on Kirchhoff's Theorem for Almost Complex Sp…
This master's project consists of verifying that the solution of the G_2-heterotic system built in the article 'The heterotic G2 system on contact Calabi-Yau 7-manifolds' is a Courant algebroid, as defined in the article 'Ricci flow, Killing spinors, and T-duality ingeneralized geometry'. If so, we can speak of the generalized Ricci curvature of this object, and the aim is to calculate it…
(Only some records are available in English at this moment)
The candidate would like to visit Johannes Nordström at the University of Bath from 01/09/2025 to 31/01/2026 to discuss his article with Diarmuid Crowley New invariants of G_2-structures, which is central to the candidate's master's degree. In this paper, Crowley and Nordström define the nu-invariant and the xi-invariant of G_2-structures and demonstrate that these invariants classify all…
This proposal studies solutions of two geometric flows, one of G2-structures, and one of Hermitian metrics on vector bundles, in order to further the study of G2-manifolds and their gauge theory. Thefirst part, building on the examples in the candidate's previous work, will be to establish an elliptic deformationtheory for solutions of the so-called Hermitian-Yang-Mills heat-flow over asy…
The aim of this proposal is to investigate the heterotic string equations in dimension 7, which are known as the G2 -Strominger system, using geometric flow techniques, as a counterpart of the Hull-Strominger system in dimension 6, which are critical points of the so-called anomaly flow.The main goal of this proposal is to describe the G2 -Strominger system in terms of the geometric invar…
This work intends to generalize a work of Da Rong Cheng, which characterizes the local minimizers of the abelian Yang-Mills-Higgs functional in terms of the so called vortex equations on the 2-sphere and the 2-dimensional torus. Being aware of the existence of a generalization of the vortex equations to Kahler manifolds, our aim is to obtain such a characterization of minimizers when the …
This Research Internship Abroad (BEPE)'s project will focus on the study of Machine Learning techniques applied to problems in Complex Differential and Algebraic Geometry. The candidate will join Professor Yang-Hui He's research group at City, University of London; and study possible continuations of the technique proposed in AHO20 for machine learning the Calabi-Yau metric on projective …
(Only some records are available in English at this moment)
| 2 / 2 | Ongoing grants |
| 8 / 8 | Completed research grants |
| 10 / 10 | Ongoing scholarships in Brazil |
| 17 / 17 | Completed scholarships in Brazil |
| 2 / 2 | Ongoing scholarships abroad |
| 7 / 7 | Completed scholarships abroad |
| 46 / 46 | All research grants and scholarships |
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