Analytic quasiperiodic matrix cocycles
Svetlana Jitomirskaya

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.