Math 348: Current Research in Analysis: Applied Harmonic and Multiscale Analysis
AbstractThe overarching theme is applied multiscale harmonic analysis, in various of its forms. Very rough outline (probably over-ambitious): - Basic Fourier analysis; Littlewood Paley theory (a.k.a. how to do multiscale analysis with Fourier); square functions & Khintchine inequality; applications to signal processing (audio/video) - Classical multiresolution analysis through wavelets; applications to Calder\'on-Zygmund integral operators and associated numerical algorithms; applications to signal processing (audio/video) - Laplacian, heat kernels and eigenfunctions on manifolds; applications to bi-Lipschitz parametrizations of rough manifolds - Laplacian, heat kernels, random walks and eigenfunctions on graphs - Multiscale analysis of random walks on graphs; applications to analysis of high-dimensional data sets, regression and inference. - A sketch of some techniques in multiscale geometric measure theory, in particular the geometric version of square functions + concentration phenomena for measures in high-dimensional spaces + results in random matrix theory. Applications to analysis of high-dimensional data sets and inference, as well as numerical linear algebra.Course page: www.math.duke.edu/~mauro/teaching.html Mail comments and suggestions concerning this site to dgs-math@math.duke.edu Last modified: |
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 Mathematics
DepartmentDuke University, Box 90320 Durham, NC 27708-0320 | |
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