speaker: yiqian wang from nanjing university
zoom id: 87863513301, code: 398342
title: on quasi-periodic schrodinger operators with cos-type potentials
abstract: quasiperiodic schrodinger operators (qpso) is the mathematical model for the conductivity on quasi-crystals which was found by a nobel prize winner. several great mathematicians have been captivated by this field.in last decades, various methods have been developed in the study of one-dimensional analytic qpso, which led to a lot of deep result. however, these methods depend heavily on analytic conditions and are difficult to be extended to smooth situations. recently we obtained a series of sharp results for sinai's model (qpso with a c^2 cos-type potential and a large coupling) . more precisely, they include a sharp estimate on the regularity of lyapunov exponents (which is even new for almost mathieu operator with a cosine potential), the dry version of cantor spectrum, homogenous spectrum gap and absolute continuity of ids.
