Taylor formulas for geometric structures

• Grant number: 25/10187-8
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: October 01, 2025
• End date: September 30, 2026
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Henrique Nogueira de Sá Earp
• Grantee: Lucca Severino Delboni
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated research grant: 21/04065-6 - BRIDGES: Brazil-France interplays in Gauge Theory, extremal structures and stability, AP.TEM

Abstract

This project proposes a, partially original, investigation into the topic of geometric structures, viewed as stabilized tensors by a reduced structure group, following the unifying approach presented by Daniel Fadel, Eric Loubeau, Andrés J. Moreno, and Henrique N. Sá Earp in 2024. The goal is to obtain Taylor formulas for tensors associated with Spin(7)-structures and U(m)-structures, analogous to those obtained by Shubham Dwivedi, Panagiotis Gianniotis, and Spiro Karigiannis in 2025 for the case of G2-structures, based on the well-known example for the Riemannian metric. The project will be carried out during the candidate's final undergraduate year and aims to deepen his mathematical training through the study of scientific articles, introducing him to contemporary geometric tools. (AU)