Generalized Spin(7) Geometry

• Grant number: 25/21756-3
• Support Opportunities: Scholarships abroad - Research Internship - Doctorate
• Start date: January 11, 2027
• End date: July 10, 2027
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Henrique Nogueira de Sá Earp
• Grantee: Bernardo Santos Vieira
• 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: 24/09514-1 - Generalized Spin(7) geometry, BP.DR

Abstract

This BEPE project consists of a research visit to Professor Mario García-Fernández at the Universidad Autónoma de Madrid (UAM). The work focuses on constructing explicit examples of heterotic and coupled Spin(7) systems and adapting moduli space techniques developed for these systems in the SU(n) and G2¿ settings to the Spin(7) case, thereby advancing the understanding of their solution spaces. The project also aims to extend constructions involving products of Sasakian manifolds to obtain solutions of the coupled Hermitian-Einstein system, and to explore the possibility of adapting the moment map framework of García-Fernández, Rubio and Tipler to develop a Seiberg-Witten-type system in higher dimensions whose moduli space is already compact, analogous to the classical Seiberg-Witten moduli space in dimension four. (AU)