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Singular G2-instantons over twisted connected sums

Grant number: 15/50368-0
Support Opportunities:Regular Research Grants
Duration: March 01, 2016 - August 31, 2017
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Geometry and Topology
Convênio/Acordo: 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


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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Scientific publications
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
JACOB, ADAM; EARP, HENRIQUE SA; WALPUSKI, THOMAS. Tangent cones of Hermitian Yang-Mills connections with isolated singularities. MATHEMATICAL RESEARCH LETTERS, v. 25, n. 5, p. 1429-1445, . (15/50368-0, 14/24727-0)

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