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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