From the heat equation to Fourier modes and Wavelets on R^n, manifolds and graphs

Mauro Maggioni, Yale University

We will quickly overview (very!) classical connections between the heat equation on R^n and Fourier and wavelet analysis. These connections generalize naturally to manifolds and graphs: we will briefly introduce the Laplacian on these structure, and discuss some properties of the associated eigenfunctions (Fourier modes). Finally, we will hint at how to construct multiscale decompositions and wavelets via the heat equation on manifolds and graphs, which will be the main topic of the afternoon talk