Video Lectures

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The dynamics associated with mechanical Hamiltonian flows with smooth potentials that include sharp fronts may be modeled, at the singular limit, by Hamiltonian impact systems: a class of generalized billiards by which the dynamics in the domain’s...

I will describe some new "coarse-graining" methods in quantitative homogenization and how they can be used to give rigorous versions of certain heuristic "renormalization group" arguments in physics, with a focus on several examples.

A fractal uncertainty principle (FUP) roughly says that a 
function and its Fourier transform cannot both be concentrated on a 
fractal set. These were introduced to harmonic analysis in order to 
prove new results in quantum chaos: if eigenfunctions on...