Yi Pan (IST Austria):
Reducibility of quasi-periodic cocycles valued in symplectic groups

Reducibility of quasi-periodic cocyles valued in symplectic groups is related to the spectrum of discrete Schrödinger operators on strips. We will talk about a global reducibility result: given one parameter families of such cocycles, for almost every one parameter, either the maximal Lyapunov exponent is positive, or the cocycle is almost reducible to some model. The techniques of the proof combine Kotani thoery, KAM theory and study of hyperbolicity of renormalization operator. This is a joint work with Artur Avila and Raphaël Krikorian.