Isospectrality of nilmanifolds

• Grant number: 24/20086-1
• Support Opportunities: Scholarships in Brazil - Master
• Start date: August 01, 2025
• End date: February 28, 2027
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Viviana Jorgelina Del Barco
• Grantee: Marcos do Nascimento Paes
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

This research project seeks to investigate the geometry of nilpotent Lie groups and the analytic properties of their compact quotients. Specifically, a primary objective is to elucidate a theorem that establishes conditions for two Riemannian nilmanifolds to be isospectral. This enables the construction of examples of such manifolds and, therefore, the analysis of geometric properties that are preserved or not under isospectrality, including the existence of integrable geodesic flow. Subsequently, we will explore the feasibility of constructing a pair of isospectral nilmanifolds, one of which admits a purely coclosed invariant G2-structure, while the other does not.