Special geometries and calibrated submanifolds

• Grant number: 21/08026-5
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: November 01, 2021
• End date: October 31, 2025
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Henrique Nogueira de Sá Earp
• Grantee: Andrés Julián Moreno Ospina
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated research grant: 18/21391-1 - Gauge theory and algebraic geometry, AP.TEM
• Associated scholarship(s): 23/13780-6 - G2-Strominger system and anomaly flow, BE.EP.PD

Abstract

The aim of this proposal is to investigate problems related with calibrated submanifolds and geometric flows on manifolds with special geometric structures. Mainly, for manifolds with G2 and SU(n) structures, using variational methods and geometric analysis tools.The first goal of this proposal is to analyse the harmonic G2-structures on almost Abelian Lie groups. This stage consists in describing the harmonic equation in terms of the Lie algebra structure, which shall lead to characterise the harmonicity with respect to the Lie bracket. Later, the corresponding gradient flow will be considered, aiming to prove the existence and convergence of invariant solutions. Further on, due to the exceptional importance of SU(n)-structures, as well as from the physical and mathematical points of view, with the study of holonomy groups and supersymmetry, we propose to develop the notion of harmonic SU(n)-structures, by applying variational theory and geometric flows methods. The second part of the project search for an advance in the research of associative submanifolds, owing to their connection with the deformation theory of singular G2-instantons. The main target is to characterise the associative submanifolds of the Stiefel manifold, as well as to describe their deformation problem. (AU)

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)

FADEL, DANIEL; LOUBEAU, ERIC; MORENO, ANDRES J.; SA EARP, HENRIQUE N.. Flows of geometric structures. JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, v. N/A, p. 86-pg., 2024-09-03. (21/04065-6, 18/21391-1, 21/08026-5)