Title: Homogenization, dispersion and effective equations
Speaker: Fabricio Macia
Speaker Info: Universidad Politécnica de Madrid.
Homogenization is a set of techniques used to study differential equations with highly oscillating coefficients. In many cases, solutions to such equations can be approximated by those of a homogeneous equations (meaning in this context an equation with constant or slowly varying coefficients) called the effective equation which is simpler to analyze. In this talk we shall present some examples arising from geometry and physics, focusing mainly on the Schrödinger equation with a periodic, highly oscillating, potential. We review some results in the literature, both in the deterministic and random frameworks, and, if time permits, present a new geometric approach to the problem, obtained in collaboration with V. Chabu and C. Fermanian-Kammerer, based on quantifying the lack of dispersion for certain evolution equations.Date: Tuesday, April 12, 2016