Veronique Fischer

High-Frequency Analysis for Subelliptic Operators

The aim of this talk is to present recent developments in the high-frequency analysis of subelliptic operators arising in sub-Riemannian geometry and related settings. Unlike elliptic operators, subelliptic operators reflect an underlying non-isotropic and non-commutative geometry, which leads to new analytical phenomena at high frequencies. I will begin by explaining why these questions are naturally connected to harmonic analysis, through nilpotent approximations, representation theory of Lie groups, and adapted notions of symbols. This perspective motivates the development of pseudodifferential and microlocal tools tailored to filtered manifolds.