4:00 pm Thursday, October 29, 2009

Michael Goldstein (University of Toronto)

In this talk we give an exposition of the ideas, methods and techn
ological tools developed in last ten years for the analysis of one-dimensional d
iﬀerence Schroedinger equations with potentials generated by shift and sk
ew-shift H(x, ω)ϕ (n) ≡ −ϕ(n − 1) − ϕ
;(n
+ 1) + V (Tω^n(x))ϕ(n) = Eϕ(n) , n ∈ Z. Here Tω is
a shift Tω (x) = x + ω, x, ω ∈ Tν , or a skew-shift,
Tω (x, y) = (x + ω, y + x), (x, y) ∈ T^2 , ω ∈ T, and
T^nω , n ∈ Z, stands for the n-th iteration of T . We state also the
central open problems in this ﬁeld.