Laplacian on homogeneous spaces

• Grant number: 24/08127-4
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: October 01, 2024
• End date: March 31, 2026
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Agreement: ANR
• Principal Investigator: Lino Anderson da Silva Grama
• Grantee: Paul Valentin Schwahn
• 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 research project is set to investigate the spectrum of Laplace operators on compact Riemannian homogeneous spaces, most prominently the Lichnerowicz Laplacian which is a natural generalization and unification of various Laplace-type operators. The analysis of the spectrum - in particular calculation of the first few eigenvalues and discussion of stability for Einstein metrics - shall be achieved using Fourier analysis, Lie-theoretic and computational methods. The project will specialize to different cases such as normal homogeneous spaces and the Kähler-Einstein metrics on flag manifolds, a continuation of the research begun in 2023. The same framework is also viable to study Killing tensors, which are candidates for eigentensors to low eigenvalues but also of independent interest. Another proposed subproject is to determine efficient multiplicity formulae for Laplace eigenspaces on some concrete compact homogeneous spaces with the aid of machine learning. (AU)