Bachelor in Mathematics (2001) and Masters in Applied Mathematics (2002) at Universidade Federal do Rio de Janeiro, Part III of the Mathematical Tripos in Theoretical Physics at University of Cambridge (2004) and PhD in Mathematics at Imperial College London (2009), supervised by Sir Simon K. Donaldson. Has experience in Differential Geometry, Geometric Analysis, Algebraic Geometry, and Mathematical Physics, focusing on the following subjects: gauge theory in higher dimensions, manifolds with special holonomy and nonlinear partial differential equations. Also interested in String/M-theory and Information Theory. Executive Manager of 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…
Professor Dragomir will take part in all scientific activities of research group Gauge Theory and Algebraic Geometry (GTAG) led by Prof. Marcos Jardim and composed by Profs Henrique Sá Earp, Rafael Leão and Simone Marchesi, as well as 4 postdoc and about a dozen graduate students.Dragomir will join our weekly research seminars and will offer a graduate course on Characteristic classes. We…
(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 doctorate research project will address the application of machine learning techniques to problems in complex differential and algebraic geometry. On a first track, the candidate will study the technique proposed in [AHO20] for machine learning the Calabi-Yau metric on projective threefolds; and will try to adapt this technique to numerically produce special G_2-metrics on the 7-mani…
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)
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 project aims to study the construction of quaternions and octonions and their relationship with the binary cross product in three and seven dimensions. The materials used as reference will be the articles "The octonions", by John C. Baez, "Notes on the octonions", by Dietmar A. Salamon and Thomas Walpuski, "Stetige Lösungen linearer Gleichungssysteme", by Beno Eckmann, and "Vector cr…
This project consists in the calculation of the partition function as outlined by Zabzine in (PRZ17,IQRZ20) on contact Calabi-Yau manifolds in (CADSE20,PSE19). The candidate will study these papers, seeking to understand the relation between these areas, and will apply what he learns to do this calculation, which, if successful, can be published as original research. (AU)
(Only some records are available in English at this moment)
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 …
This BEPE project consists of a research visit by the candidate to Professor Jason Lotay at Oxford University with the main goal to discuss certain aspects of his joint paper with the project's advisor. In the aforementioned paper, the authors constructed non-trivial solutions to the heterotic G2-system on certain contact Calabi-Yau 7-manifolds. The motivation to understand their construc…
This BEPE project consists of a research visit by the candidate to Professor Mario Garcia-Fernandez at Universidad Autónoma de Madri with the main goal to discuss certain aspects of his papers and his work in generalized geometry in general. In the aforementioned papers, the author introduces the primordial concepts of generalized geometry and proposes the analogue definitions of Ricci cu…
In this internship, the candidate will calculate partition functions for supersymmetric Yang-Mills theory on Calabi-Yau links. This internship follows one at Oxford in which the candidate will have studied the mathematical side of Calabi-Yau links and mapped the necessary procedure to do this calculation. (AU)
(Only some records are available in English at this moment)
| 3 / 3 | Ongoing research grants |
| 7 / 7 | Completed research grants |
| 6 / 6 | Ongoing scholarships in Brazil |
| 13 / 13 | Completed scholarships in Brazil |
| 2 / 2 | Ongoing scholarships abroad |
| 4 / 4 | Completed scholarships abroad |
| 35 / 35 | All research grants and scholarships |
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