We consider an energy model for N ordered elastic membranes
subject to forcing and boundary conditions. The heights of the
membranes are described by real functions u_1, u_2,...,u_N, which
minimize an energy functional involving the Dirichlet...
We study multiply warped product geometries
MN:=Bn×Fn1×···×FnA
g = g_B + \sum_{a=1}^A v_a^2 g_{F^{n_a}} and show that for an
open set of initial data within multiply warped product geometries
the Ricci flow starting at any of those develops...
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...
