Complexity of the geometry, randomness of the potential, and
many other irregularities of the system can cause powerful, albeit
quite different, manifestations of localization, a phenomenon of
sudden confinement of waves, or eigenfunctions, to a...
I will explain a proof of a joint with D. Alvarez-Gavela and D.
Nadler theorem which allows to make a Lagrangian submanifold
transverse to a given Lagrangian distribution in exchange for
making them piecewise smooth with canonical singularities...
We consider variational principles related to V. I. Arnold's
stability criteria for steady-state solutions of the
two-dimensional incompressible Euler equation. Our goal is to
investigate under which conditions the quadratic forms defined by
the...