4:00 pm Thursday, October 29, 2009
Colloquium: Schroedinger equations with potentials generated by shifts and skew-shifts
by Michael Goldstein (University of Toronto) in HB 227
In this talk we give an exposition of the ideas, methods and technological tools developed in last ten years for the analysis of one-dimensional difference Schroedinger equations with potentials generated by shift and skew-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. Host Department: Rice University-Mathematics Submitted by dani@rice.edu |