G2-Strominger system and anomaly flow

• Grant number: 23/13780-6
• Support Opportunities: Scholarships abroad - Research Internship - Post-doctor
• Start date: March 01, 2024
• End date: February 28, 2025
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Henrique Nogueira de Sá Earp
• Grantee: Andrés Julián Moreno Ospina
• Supervisor: Mario Garcia Fernandez
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Institution abroad: Instituto de Ciencias Matemáticas (ICMAT), Spain
• Associated to the scholarship: 21/08026-5 - Special geometries and calibrated submanifolds, BP.PD

Abstract

The aim of this proposal is to investigate the heterotic string equations in dimension 7, which are known as the G2 -Strominger system, using geometric flow techniques, as a counterpart of the Hull-Strominger system in dimension 6, which are critical points of the so-called anomaly flow.The main goal of this proposal is to describe the G2 -Strominger system in terms of the geometric invariants of the associated (locally) conformal coclosed G2 -structure, such as its curvature and the torsion tensor. This formulation shall provide a picture about the parabolicity of the corresponding G2-anomaly flow, as it has been done for many geometric flows in G2 -geometry. This will allow one to address analytical questions for the flow, such as existence and convergence under particular torsion constraints.Later, the G2 -anomaly flow can be study in the context of homogeneous manifolds, where the symmetries of space reduces the geometric flow to an ODE. Working in this context could lead to an interesting study of the qualitative behavior of the G2 -anomaly flow, as well as the convergence of solutions in Gromov-Hausdorff topology.