| Processo: | 15/50368-0 |
| Linha de fomento: | Auxílio à Pesquisa - Regular |
| Vigência: | 01 de março de 2016 - 31 de agosto de 2017 |
| Área do conhecimento: | Ciências Exatas e da Terra - Matemática - Geometria e Topologia |
| Convênio/Acordo: | MIT |
| Pesquisador responsável: | Henrique Nogueira de Sá Earp |
| Beneficiário: | Henrique Nogueira de Sá Earp |
| Pesq. responsável no exterior: | Thomas Walpuski |
| Instituição no exterior: | Massachusetts Institute of Technology (MIT), Estados Unidos |
| Instituição-sede: | Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brasil |
| Assunto(s): | Teoria de Gauge Singularidades Equações de Yang-Mills Cooperação técnica Cooperação internacional |
Resumo
We propose a collaboration between Marcos Jardim, Henrique Sá Earp, Gregoire Menet and Lazaro Díaz (Unicamp) and Tomasz Mrowka and Thomas Walpuski (MIT) to advance the understanding of gauge theory on G2-manifolds obtained as a twisted connected sum, with a focus on singularities. G2-geometry, in general, and our project, in particular, stand at the crossroads of Algebraic Geometry, Differential Geometry, Topology, Geometric Analysis and Theoretical Physics. Our main goals are: - to prove a correspondence between singular HYM connections and reflexive sheaves, following the works of Sá Earp and Bando & Siu, and understand their deformation theory. - to calculate the Donaldson-Thomas invariant conjectured by Walpuski as a transversal Lagrangian intersection, in some favourable cases, using the work of Menet. - to generalise the construction of topological associative submanifoids, by Díaz, Nordstrom and Sá Earp. (AU)