| Grant number: | 15/50368-0 |
| Support Opportunities: | Regular Research Grants |
| Start date: | March 01, 2016 |
| End date: | August 31, 2017 |
| Field of knowledge: | Physical Sciences and Mathematics - Mathematics - Geometry and Topology |
| Agreement: | MIT |
| Principal Investigator: | Henrique Nogueira de Sá Earp |
| Grantee: | Henrique Nogueira de Sá Earp |
| Principal researcher abroad: | Thomas Walpuski |
| Institution abroad: | Massachusetts Institute of Technology (MIT), United States |
| Host Institution: | Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil |
Abstract
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)
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