Abstract
The project aims to study the F-manifolds structures on the orbit spaces of reflection groups (AU)
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Igor Mencattini
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: Itália
Ph.D. in Mathematics from Boston University (2005). Has experience in Mathematics, acting on the following subjects: fisica matematica. (Source: Lattes Curriculum)
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Research grants
- Deformations of Poisson-Nijenhuis strucures, AV.EXT
Abstract
The aim of this project is to investigate the deformations of Poisson- Nijenhuis structures induced by a two-form satisfying a suitable integrability condition. From a strictly geometrical point of view these deformations are naturally related to the gauge transformations of the Dirac structures underlying the original Poisson- Nijenhuis manifold. On the other hand from the view point of …
- Hamiltonian aspects of almost-intertwining matrices, AV.EXT
Abstract
The project aims to recast the analysis of the complete integrability of the q-deformed rational Calogero-Moser system in the framework of the Hamiltonian reduction and, more generally, to study the correspondence between rank-one condition and integrable systems from the point of view the Hamiltonian formalism. (AU)
- Combinatorial Hopf algebras in pure and applied mathematics, AV.EXT
Abstract
This research project aims at a deeper understanding of the mathematical aspects of a class of Hopf algebras of combinatorial type. The central object of this project is a family of closely related Lie admissible algebras known as pre-Lie algebras. More precisely, we aim to study the Hopf sub-algebra of the circle rooted trees that play the same role as the Hopf sub-algebra of ladder gra…
(Only some records are available in English at this moment)
Scholarships in Brazil
- About a theorem by Nomizu, BP.MS
Abstract
This project aim to analyze some of the existing relations between homogenous spaces and non-associative algebras. The case of reductive homogenous spaces will be studied in details.
- Simple Lie algebras and their classification, BP.IC
Abstract
This project aims to introduce the theory of finite-dimensional, semi-simple Lie algebras, emphasizing both classification and the construction of explicit models of these algebraic structures.(AU)
- A bird's-eye view of category theory, BP.IC
Abstract
This project has a main goal to introduce the basics concepts of category theory and some of its applications.
- Prequantization and extensions, BP.MS
Abstract
In this project we will study some aspects of Lie theory and some of its interactions with symplectic geometry. In particular we will investigate under which assumptions a connected Lie group G acting on a connected symplectic manifold (M,É) via symplectomorphisms, admits a central extensions G2 acting as a group of symmetries of a pair (L,±) of a principal R/D-bundle, where D is a discre…
(Only some records are available in English at this moment)
Scholarships abroad
- Cluster algebras and integrable systems, BE.EP.DR
Abstract
Since the inventions of cluster algebras (2001) by S. Fomin and A.Zelevinsky, motivated for the study of dual canonical bases and total positivity in semisimple groups, relations with Poisson geometry and Integrable systems were developed. The notion of Poisson bracket compatible with a cluster structure, introduced by M.Gekhtman, M.Shapiro and A.Vainshtein, was used to interpret cluster …
Total / Available in English
| 1 / 1 | Ongoing grants |
| 6 / 6 | Completed research grants |
| 1 / 1 | Ongoing scholarships in Brazil |
| 9 / 9 | Completed scholarships in Brazil |
| 1 / 1 | Completed scholarships abroad |
| 18 / 18 | All research grants and scholarships |
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