Abstract. 
Analytic quasiperiodic matrix cocycles are simple dynamical
systems, where analytic and dynamical properties are related in an
unexpected and remarkable way. We will focus on this relation, leading to
a new approach to the proof of joint continuity of Lyapunov exponents in
frequency and cocycle, at irrational frequencies, first proved for SL(2,C)
cocycles in Bourgain-Jitom., 2002. The approach is powerful enough to
handle singular and multidimensional cocycles, thus establishing the above
continuity in full generality. This has important consequences including
a dense open version of Bochi-Viana theorem in this setting, with a
completely different underlying mechanism of the proof. A large part of
the talk  is a report on a joint work with A. Avila and C. Sadel.