Schodinger Operator and Avila's work on Quasi-periodic Analytic SL(2,R) Cocycles.

In this talk, the plan is to take the opportunity to introduce some results of Avila on quasi-periodic one-frequency analytic Schrodinger operators. This should be a working seminar talk, given by a non expert in the field, in the hope of attracting interests of more people to look at this area. We hope to be able to describe the so called Avila's "global theory" and also comment on some connections with new results in dynamics.